After a flying saucer lands in Washington, D.C., the United States Army quickly surrounds it. A humanoid emerges and announces that he comes "in peace and with good will". When he unexpectedly opens a small device, he is shot and wounded by a nervous soldier. A tall robot emerges from the saucer and quickly disintegrates the soldiers' weapons. The alien orders the robot, Gort, to desist. He explains that the now-broken device was a gift for the President of the United States that would have enabled him "to study life on the other planets".
The alien, Klaatu, is taken to Walter Reed Army Hospital. After surgery, he uses a salve to quickly heal his wound. The Army is unable to enter the saucer. Gort stands outside, silent and unmoving.
Klaatu tells the President's secretary, Mr. Harley, that he has a message that must be delivered to all the world's leaders simultaneously. Harley tells him that in the current world situation, this is impossible. Klaatu proposes that he spend time among ordinary humans to better understand their "unreasoning suspicions and attitudes". Harley rejects the proposal, and Klaatu remains locked in his hospital room.
Klaatu escapes and stays in a boarding house using the name Mr. Carpenter, adopted from a dry cleaner's suit tag. Among the residents are young widow Helen Benson and her son Bobby. Helen's boyfriend, Tom Stevens, becomes jealous of the stranger.
Bobby takes Klaatu on a tour of the city, including a visit to his father's grave in Arlington National Cemetery; Klaatu learns that most of the dead are soldiers killed in wars. They also visit the Lincoln Memorial. When Klaatu asks Bobby, "Who is the greatest living person?", Bobby suggests Professor Barnhardt. They visit the scientist's home, but he is out; Klaatu sees that Barnhardt's blackboard is covered with equations (an attempt to solve the three-body problem). Klaatu adds to them and, after being discovered by the housekeeper, leaves his contact information.
That evening, a government agent escorts Klaatu to Barnhardt. Klaatu tells Barnhardt that the people of other planets are concerned about Earth's possible aggression, now that humanity has developed rockets and rudimentary atomic power. He states that if his message is ignored, Earth could be "eliminated". Barnhardt agrees to gather scientists from around the world at the saucer; he also suggests that Klaatu peacefully demonstrate the power he possesses beforehand.
Klaatu returns to his spaceship, unaware that Bobby is following him. Bobby watches as Gort knocks out two soldiers so Klaatu can reenter the saucer. Bobby runs home and tells Helen. She does not believe him, but Tom is suspicious.
The next day, for half an hour, starting at 12 noon east coast time, all electrical equipment on Earth ceases to function,[7] except for essential services, such as hospitals and aircraft in flight.
Klaatu learns that Bobby watched him the previous night. He visits Helen at work, reveals his mission, and asks that she not betray him. Helen asks Tom to keep Klaatu's identity secret, but he refuses to listen, already in the process of alerting the military.
Helen and Klaatu rush to Barnhardt's home. They hope that Barnhardt can hide Klaatu until the meeting that evening. Klaatu tells Helen that if anything should happen to him, she must go to Gort and say, "Klaatu barada nikto."
The Army tracks them in their taxi. Klaatu is shot and killed, and his body is moved to a nearby police station cell. Helen rushes to the saucer and says Klaatu's phrase to Gort. Gort retrieves Klaatu's body, and revives him inside the saucer, though Klaatu tells Helen that his revival is only temporary.
Helen departs the spaceship with Klaatu and Gort, joining Dr. Barnhart among the gathered scientists. Klaatu tells the scientists gathered outside that an interplanetary organization has created a police force of invincible robots like Gort. "In matters of aggression, we have given them absolute power over us". Klaatu concludes, "Your choice is simple: join us and live in peace, or pursue your present course and face obliteration. We shall be waiting for your answer." Klaatu and Gort depart in the saucer.
