The opening scene shows Dr. Kathy Grieff (Jennifer Jason Leigh) entering a secured room. She is there to meet with Morgan (Anya Taylor-Joy), and the whole thing is seen through surveillance cameras. Kathy sits down to have lunch with Morgan. Morgan looks at her own hands curiously on both sides as Kathy says she couldn't get "them" to let Morgan go outside. Morgan pushes aside everything on the table, jumps over it, and begins to stab Kathy in the eye. Two other doctors enter to intervene and sedate Morgan.
Lee Weathers (Kate Mara), a risk management consultant, travels to the facility where the incident took place. She meets Amy Menser (Rose Leslie), Morgan's behaviorist, and Skip Vronsky (Boyd Holbrook), the team's nutritionist. Lee then goes to meet Dr. Simon Ziegler (Toby Jones), who explains to her the creation of Morgan. After two failed experiments, Morgan was a creation of synthetic life that matured at a rapid rate over six months, where she now maintains the appearance of a young woman. Lee is also shown a video of the incident, showing that Morgan has managed to develop emotions as well. She has spent most of her time with Amy, who treats Morgan like a sister.
Lee meets Kathy in her room, where she is heavily medicated and wearing a pad over her wound. She blames herself for what happened and says she provoked Morgan into attacking her. Kathy tells Lee that Morgan was once full of joy before she was put back into her room. Morgan was allowed exposure to the outside world at a young age, which the others think was a mistake. As Kathy refers to Morgan by female pronouns, Lee says that Morgan should be referred to as "it".
Lee is brought in to meet Morgan personally. She is kept outside of Morgan's room for protection. Morgan already knows who Lee is and appears polite, but also highly intelligent. Afterwards, Ziegler asks Lee if she's impressed. Lee looks pretty unimpressed, which appears to displease Ziegler.
That night, Lee joins the team for dinner and meets others such as Drs. Darren and Brenda Finch (Chris Sullivan and Vinette Robinson), Ted Brenner (Michael Yare), and Dr. Lui Cheng (Michelle Yeoh), whom Lee regards highly and whom Morgan considers to be her "mother". Later on, Lee is outside talking to Skip, who's had a bit to drink. Amy overhears their conversation, where Skip tells Lee that he and Amy had a fling before realizing he wasn't her type. He makes a move by kissing Lee, but then apologizes for it afterwards. Amy walks away to Morgan's cell to spend time with her after turning off the cameras.
We see a flashback of Amy taking Morgan out into the woods for fresh air. Amy tells Morgan about trees and how some live to be thousands of years old. The two then see a deer that's been impaled in the side. Morgan breaks its neck out of mercy.
The next day, Morgan is set for a psych analysis by Dr. Alan Shapiro (Paul Giamatti). Shapiro is supposed to sit outside of Morgan's room, but he finds that pointless and decides to go inside. He starts to talk to Morgan calmly before going off and yelling at her, asking her how she would react if she told the doctors to put her back in the box and never let her out, or if she should be terminated. Morgan sheds tears and says she doesn't know what to do. She looks at her hands on both sides until she reaches her breaking point. Morgan pushes Shapiro against the wall and lunges at him, biting hard into his throat and ripping a chunk out. The doctors try to go in and sedate Morgan, but she escapes. Lee grabs a tranquilizer and follows her outside. Morgan gets outside but only finds Amy, who sees her face caked in blood, right before Lee hits her with a dart.
Morgan is strapped to a table to be terminated. She tearfully pleads with the doctors to not go through with it, even calling Dr. Cheng "Mother". She coldly responds that she is not Morgan's mother. Morgan is sedated and she passes out. Darren gets a needle ready to give her a lethal injection, but he refuses to go through with it. Cheng leaves the room and wipes away a tear. Lee decides to do it herself. She enters the room, but Ted tries to stop her. Lee hits Ted in the face repeatedly and nearly shoots him with a pistol, but she gets hit with a dart herself.
Darren, Ted, and Brenda try to get Morgan out of there. Darren tries carrying her as she's out, but Morgan wakes up and headbutts Darren in the face. She grabs the needle he would have injected her with and sticks it in his chest, killing him. Morgan then grabs the pistol and shoots Ted once, which Lee sees as she wakes up. Morgan then shoots Ted in the head before retreating and leaving Lee locked in her room.
Morgan goes into Kathy's room and kicks her in the face until she snaps her neck. She also kills Zielger by hanging him. Morgan then makes her way into Cheng's room as she finishes making a video confession. Morgan suffocates Cheng to death.
Brenda gets Amy and tries to make a run for it. Morgan appears with the gun and aims it at Brenda. Brenda punches Morgan in the face and fights her, but Morgan overpowers her and proceeds to beat Brenda to death.
Lee breaks out of the room by climbing to the top and smashing the glass. She meets up with Skip, who tells her not to follow Morgan. Lee gets in her car and chases after Morgan and Amy as they drive away, knowing where they're headed. Lee chases them though the woods, but Morgan causes Lee to crash into a tree. Skip drives up and drives Lee to find them.
Lee takes Skip's rifle and tries to kill Morgan herself. Morgan catches up to Lee and fights her in the woods. After getting a few good punches and kicks in, Morgan pushes Lee to the ground where she gets impaled by a root. Morgan leaves her and rejoins Amy by the lake, which she is in awe of. Lee shows up after pulling herself out, and she pushes Morgan into the lake. Lee then holds Morgan underwater until she drowns. Lee gets out of the water and then shoots Amy with the pistol. She gets back to Skip and kills him too.
The company's head, Jim Bryce (Brian Cox), declares the Morgan project a failure. His associate asks, "What about Lee Weathers?" Bryce replies, "What about her? She's perfect."
The last shot is of Lee looking at her hands on both sides...JUST LIKE MORGAN!