In Washington, D.C. in the year 2054, John Anderton (Tom Cruise) and his team of "Precrime" police officers are in the midst of locating a suspect who is about to commit a murder. They are acting on data obtained from the "precogs," three mutated humans who can see into the future. The process involves Anderton's meticulous "scrubbing" of the images from the precogs' visions, looking for clues that reveal the location. Only the names of the victim and perpetrator, and the time and date of the crime, are explicitly given.
Anderton determines that the residential area of Sarah, the victim, and her husband Howard, the perpetrator, has a park with a merry-go-round. Howard has discovered that his wife has been cheating on him and plans to murder them both with a large pair of scissors. Anderton and his team are dispatched to the area but still have not discerned the precise address. Anderton notices that Howard left the front door open when he returned to the house for his glasses. The team rushes upstairs, stopping Howard's crime of passion just seconds before he commits it. Howard is arrested and "haloed" (a device placed around his head that renders him fully incapacitated), while his wife is counseled.
As Anderton works, he is observed by Danny Witwer (Collin Farrell), an agent from the United States Department of Justice. Witwer has been sent to evaluate the system because the country is about to vote on whether to expand the Precrime program nationally. After the suspect has been apprehended, the murder reappears on the displays. It is explained that the precogs sometimes think about a crime that has been stopped, and that these echo images are deleted from the system. 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. We also see that Anderton is also addicted to an illegal inhaled hallucinogen called Neuroin.
The next morning, he and Witwer tour 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. When Anderton investigates, he finds that the visions from the other two precogs, Arthur and Dashiell, are on record, but Agatha's is not. The potential victim, a woman named Ann Lively, was reported as having gone missing shortly after her assailant was caught. Anderton reports his findings to Precrime Director Lamar Burgess (Max von Sydow), who suggests that he let the matter drop.
Upon returning to his office, Anderton is alerted to a new murder that is to take place in 36 hours, with himself 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 auto assembly plant, using a car that is constructed around here. 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 vanished he 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 trios 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. It is identical to the one he watched in his office. The two 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 Crows 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 tries to persuade Anderton that he does not have 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.
Witwer explained to Burgess that Lively's potential killer was arrested based on the matching visions of Arthur and Dashiell, but a second person then arrived and killed her in exactly the same manner, the act seen by Agatha and later disregarded as an echo vision. 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 villain in the film, kills Dashiell, 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, Agatha's mother, 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 the prison guard to release Anderton, who then calls Burgess to reveal he's figured out his whole murderous modus operendi 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 a 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.