In Washington, D.C. in the year 2054, John Anderton (Tom Cruise) is head of a new police force called "PreCrime," which has completely eradicated murder in the DC area, by allowing the police to stop murders before they can even be committed. Data is obtained from "PreCogs," three mutated humans who can see into the future. When the PreCogs detect that a murder is going to be committed, an automated system processes two painted wooden balls: one with the name of the perpetrator(s) engraved into it, and one with the name of the victim(s) engraved into it (the system itself being designed to be tamperproof). The color of the ball indicates what kind of murder it will be: a brown ball indicates a premeditated murder, which the PreCogs can predict up to four days before it is committed. A red ball indicates a crime of passion, which, due to the lack of premeditation, cannot be seen until often no less than an hour before it will be committed.
The only three things that the PreCogs can predict are the victim or victims, the perpetrator, the exact date and time of the crime, and the exact sequence of events that lead up to the crime. They do not pinpoint the location. Thus, Anderton and his team have to perform a meticulous process called "scrubbing", where they process the images produced from the precogs' visions in order to locate telltale clues and thus narrow down the location. Once they are certain of the location, the team flies there to thwart the crime. They then secure the culprit by "haloing" him (a device placed around his head that renders him fully incapacitated).
After the suspect has been apprehended, the murder reappears on the displays. As it turns out, the PreCogs sometimes think about a crime that has been stopped, and that these "echo" images are deleted from the system.
As the movie starts, Anderton's team receives an early morning Red Ball case. The perpetrator is going to be a male in his 40s named Howard Marks, and the victims are going to be his wife Sarah and another man named Donald Dubin, and the crime is going to be committed at exactly 8:04 a.m, which is 24 minutes from now. Anderton goes to work scrubbing the visions produced by the PreCogs. The visions show that Howard is going to catch Sarah in bed with Dubin after coming back to retrieve his glasses, then will viciously stab them both to death with a pair of scissors.
Anderton learns there are six people named Howard Marks. Through facial comparison between the 'visions' and the drivers' license photos, he's able to determine which one they're after. He gives an order for the police to send a squad car to the address. However, there's a problem: Howard doesn't live there anymore as his family moved a few weeks prior and none of his old neighbors know where he lives now.
At this point, Anderton is momentarily distracted by the arrival of Danny Witwer (Colin Farrell), a Justice Department official who's been sent to audit the PreCrime system before the country votes on whether or not to take the system nationwide. One of Anderton's colleagues, Fletcher, explains to Witwer the basic workings of the system as Anderton continues analyzing the visions. He's able to identify the material used in the construction of the house's exterior. Then, by looking at the relative location of a kid in the background of two images of Dubin, he's able to determine that there is a park with a merry-go-round across the street from the future crime scene.
Having narrowed down the location, Anderton and his team get into their flying craft and fly to the scene, arriving three minutes before the crime is to be committed. There's a new problem now: Howard's house is just one in a row of identical houses, making it impossible to know which house is the one they need to raid. Scanning each house, Anderton notices that at one of them, the front door is ajar. He calls back to the office and gets confirmation that Howard did leave the front door open when he returned to the house for his glasses. Now certain of his target, Anderton storms into the house, runs up to the bedroom, and overpowers Howard just seconds before he can stab his wife with the scissors. As Anderton's stopwatch hits zero, the rest of his team bursts in through the skylight. Howard is identified by iris scan, and is promptly arrested and "haloed" , while his wife is immediately given counseling by a trauma response unit.
That evening, Anderton reminisces over home movies of his ex-wife Lara (Kathryn Morris) and the couple's missing six-year-old son, who disappeared several years before at a public swimming pool. Anderton is also shown to have an addiction to an illegal inhaled hallucinogen called Neuroin (New Heroin).
The next morning, Witwer's official tour of the Precrime headquarters begins. Throughout the tour, Witwer points out there are potential questions about the ethics of the PreCogs. Anderton explains that the system is designed in a way to be practically foolproof, due to the nature of premeditation and the fact that the PreCogs see what the killer will do, not what they intend to do. At Witwer's insistence, Anderton takes him into the chamber in which the precogs are kept semiconscious in a pool of fluid similar to amniotic fluid and are wired to the Precrime computer system. After Witwer has gone, the precog Agatha (Samantha Morton) snaps fully awake, and images of a woman being murdered play across the chambers video screens.
Curious as to what he's seen, Anderton goes down to Containment, where numerous other haloed Precrime assailants are kept. With the aid of a supervisor named Gideon (Tim Blake Nelson), Anderton finds the assailant who was in Agatha's Previs, though he is classified as a John Doe.
Gideon attempts to pull up more information on the case, but finds that of the three precogs, Agatha's Previs is missing. As well, information on just where Ann Lively is, is also missing. The only information that the computer has on her, is that she was a single mother, who was also a Neuroin addict, but records indicate she went to a rehabilitation clinic to treat her habit.
Anderton reports his findings to Precrime Director Lamar Burgess (Max von Sydow), who suggests that he let the matter drop, turning his attention towards the thought that when Precrime goes nationwide, they need to find a way to protect it from larger interests. Anderton assures his mentor that he won't let that happen.
Upon returning to his office, Anderton is alerted to a new murder that is to take place in 36 hours. To his shock, he is listed as the perpetrator. He does not know the victim, Leo Crow, leading him to believe that he is being set up. The caretaker of the precogs, Wally, sees the vision and gives John two minutes to leave the building before he hits the alarm. John escapes and is immediately chased by his own team and Witwer. Having trained his team, he has an advantage and escapes them through an apartment building and an automated auto assembly plant, using a car that is constructed around him.
He makes his way to the residence of Dr. Iris Hineman (Lois Smith), whose research laid the groundwork for the Precrime program. Quite eccentric but still coherent, Hineman explains that the three precogs do not always agree on their visions of the future; when this happens, the one that deviates the most from the others typically is ignored. In order to establish his innocence, Anderton must determine whether this "minority report" exists and, if so, get it for himself. Anderton is puzzled as to which of the precogs would generate a minority report and Hineman tells him its the "most talented" of the three: Agatha.
Since everyone is subjected to iris scans wherever they go, Anderton undergoes an eye transplant at the hands of a shady doctor. The doctor is actually one of John's past cases, whom he busted for performing questionable surgery, however, the doctor performs the procedure anyway, leaving John alone to recover.
While sleeping after the surgery, he dreams about the day his son was abducted from a swimming pool, and awakens to find the Precrime team searching the building for him. Small robotic eye scanners known as "spiders" are sent into the rooms; one of them finds Anderton and scans his iris, but the surgery has succeeded and he is not recognized. Returning to the Precrime offices in disguise, Anderton removes Agatha from the precogs chamber, disrupting the trio's hive mind that makes the system work.
He takes her to a hacker friend of his, who successfully extracts her vision of Crows murder for Anderton to see. However, the vision does not deviate from what he saw previously, and Anderton realizes that he doesn't have a minority report.
Suddenly, Agatha begins to seizure, and the image of Ann Lively being drowned is seen again. As Anderton watches the vision, his friend alerts him to Precrime officers in their vicinity. Agatha and Anderton narrowly escape Anderton's team, by making use of strategic information provided by Agatha, who is able to predict the immediate future.
Anderton tracks down Crow's address and gains entry to his apartment. Crow is not present, but he finds a pile of photographs of children, including his missing son. Anderton realizes that there is no minority report in his case and he is now going to kill Crow, whom he now blames for the kidnapping. When Crow enters, Anderton assaults him to extract a confession as Agatha pleads with Anderton not to commit this murder. Anderton is blind to her pleas and is intending to kill Crow, until the timer on his watch goes off... the time when the murder is supposed to take place. Anderton relents, and begins to read Crow his Miranda rights. Crow reveals that the photographs are doctored and were given to him to leave in the apartment in order to set up this very confrontation. His family has been promised a cash payoff only if Anderton kills him; to force this outcome, Crow grabs Anderton's gun hand, aims the weapon at himself, and pulls the trigger.
After Anderton and Agatha flee, Witwer and the Precrime team arrive to investigate the crime scene. Witwer is doubtful about the "orgy of evidence" that was left behind and later discusses his misgiving with Burgess, bringing up the Lively case as well. He now has all three precogs records of that murder, but slight differences between them lead him to deduce what really happened that day.
Witwer shows Burgess the previsions from containment, but then reveals Agatha's which was not on file. Agatha's vision shows a very big difference, leading Witwer to postulate that the crime against Anne Lively took place at two different times.
When Burgess questions Witwer, the young man posits his theory: Ann Lively's potential killer was arrested based on the matching visions of Arthur and Dashiell, but after Precrime had taken the man away, a second person (matching the same look of the potential killer), arrived and killed her in exactly the same manner. The similarity of the incidents would simply lead the precog techs to assume the act Agatha witnessed, as an 'echo' vision, and therefore, disregard it. Witwer suggests that only a member of Precrime could have the skill to manipulate the system in this way, whereupon Burgess, revealing himself as the true architect of John's framing, kills Witwer, knowing that the other precogs are unable to foresee this act with Agatha gone.
As Anderton and Agatha hide in Lara's house, he realizes that he was set up because of what he knows about the Lively case. Lively is Agatha's biological mother and had been killed because she wanted to reunite with her daughter. The police finally apprehend Anderton, halo him, and return Agatha to the precogs chamber. Burgess later meets with Lara to comfort her, but when she brings up her preoccupation about the Lively case, he inadvertently refers to it as a drowning, contradicting the official precog report and implicating him in the murder.
Lara rushes back to precog headquarters and forces Gideon to release Anderton, who then calls Burgess to reveal he's figured out his whole murderous modus operandi and then brings a reception in Burgess' honor to a frightening halt by screening for all to see the "minority report" that shows him killing Lively.
At the same time, a new potential murder is detected by the precogs, with Anderton as victim and Burgess as perpetrator. Realizing that Anderton must be somewhere nearby, Burgess takes an antique revolver given to him as a gift and searches for him. When the two men come face to face, Anderton points out he is in a Catch-22: if Burgess shoots, he will prove that Precrime works but will be haloed for life; if he doesn't shoot, the Precrime system is proven to be unreliable. Burgess resolves the dilemma by killing himself.
The Precrime program, revealed to be subject to manipulation and thus flawed, is abandoned. All criminals imprisoned under it are pardoned and released, though local police departments keep watch on many of them for years. Anderton reconciles with Lara, now pregnant with their second child, and the precogs are moved to an unnamed remote location where they can live in peace.