The film opens with a flying saucer which lands on the Ellipse in President's Park, Washington, D.C. Its pilot Klaatu (Michael Rennie) emerges and declares he has come on a mission of goodwill. When he opens a small, menacing-looking device, he is shot and wounded by a nervous soldier. In response, a large humanoid robot called Gort (Lock Martin) steps out of the ship and disintegrates all weapons present without harming the soldiers. Klaatu orders him to stop and remarks that the device he carried was in fact a gift to the President that could have been used to study life on other planets. Klaatu is taken to an army hospital, where he recovers. The military attempts to enter Klaatu's ship, but finds it impregnable, while Gort stands motionless outside.

Klaatu meets the President's secretary, Mr. Harley (Frank Conroy), and reveals he has a message he wants the whole world to hear, to which Harley replies that the divided world leaders would not even be able to agree on a meeting place. When Klaatu suggests he live among ordinary people to get to know them better, Harley informs him that he is in protective custody. Klaatu escapes to a boarding house, assuming the alias "Mr. Carpenter," the name on the laundry label of a suit he has taken. Among the residents are Helen Benson (Patricia Neal), a widow whose husband was killed in World War II, and her son Bobby (Billy Gray). The next morning, Klaatu listens to a paranoid radio commentator and to the boarders' speculations on the subject of his flying saucer over the breakfast table; one (Frances Bavier) suggests that it might be the work of the Soviets.

When Helen's boyfriend, Tom Stephens (Hugh Marlowe), plans a day trip for the two of them, Klaatu offers to babysit Bobby. Bobby takes Klaatu on a tour of the city, including a visit to his father's grave in Arlington National Cemetery, where Klaatu is dismayed to learn that most of those buried there were killed in wars. The two then visit the Lincoln Memorial and the heavily-guarded spaceship. Klaatu, impressed by the inscription of Abraham Lincoln's Gettysburg Address, is hopeful that Earth may harbor people wise enough to understand his message. When he asks Bobby to name the greatest person living in the world, Bobby suggests a leading American scientist, Professor Jacob Barnhardt (Sam Jaffe), who lives nearby. Bobby takes Klaatu to Barnhardt's home. The professor is absent, but Klaatu helps solve an advanced mathematical n-body problem written on a blackboard in the study as a means of introducing himself and leaves his address with the housekeeper.

Later, government agents escort Klaatu to see Barnhardt, who has seen the correction to his work as a calling card which could not have been faked. Klaatu warns the professor that the people of the other planets are concerned for their own safety because human beings have developed atomic power. Barnhardt offers Klaatu the opportunity to speak at an upcoming meeting of scientists he is organizing; Klaatu accepts. Barnhardt is stunned when Klaatu declares that, if his message is rejected, "Planet Earth will be eliminated." The professor pleads for Klaatu to first provide a small demonstration of his power as a warning. Klaatu returns to his spaceship the next evening to implement the professor's suggestion, unaware that Bobby has followed him.

Bobby tells Helen and Tom what he has seen when they return. At first, they do not believe him. When Bobby persists in his claims, Tom tries to find Klaatu to confirm it was just a dream; in Klaatu's room, Tom finds a diamond on the floor. Bobby casually remarks that Klaatu had given him two others for $2. The following day, Tom shows the gem to a jeweler, who declares it unique.

Klaatu goes to Helen's workplace and asks to speak to her. She leads him to an unoccupied elevator which stops suddenly. Klaatu admits he is responsible, tells Helen his true identity, and asks for her help. A montage sequence shows that Klaatu has neutralized electric power everywhere for half an hour (with the exception of critical systems such as hospitals and planes in flight), bringing the world to a standstill and thereby providing the demonstration Barnardt had suggested.

After the blackout ends, the manhunt for Klaatu intensifies and Tom tells the authorities of his suspicions. Helen and Klaatu take a taxi to Barnhardt's home; en route, Klaatu tells Helen that if anything should happen to him, she must go to Gort and say, "Klaatu barada nikto." When they are spotted, Klaatu tries to flee, but is shot dead.

Helen goes to the spaceship and approaches Gort, who awakens and kills two guards before Helen can give him Klaatu's message. Gort gently carries her into the spaceship, retrieves Klaatu's corpse, and revives him.

Klaatu steps out of the spaceship and addresses the assembled scientists, explaining that humanity's penchant for violence and first steps into space have caused concern among the other spacefaring worlds, who have created a race of robot enforcers including Gort and given them absolute power to stifle any aggression. He warns that if the people of Earth threaten to extend their violence into space, then the robots will destroy Earth, adding that "The decision rests with you." He then enters the spaceship and departs.