An extraterrestrial flying saucer is tracked streaking about the Earth until it gently lands on the President's Park Ellipse in Washington, D.C. Klaatu (Michael Rennie) emerges, announcing that he has come from outer space on a goodwill mission. Upon opening a small, suspicious-looking device, he is wounded by a nervous soldier and the device is destroyed. In response, Gort, a large humanoid robot emerges from the ship and disintegrates all weapons present with a ray emanating from his head, without harming the soldiers. Klaatu orders him to stop and explains that the ruined object was a viewing device, a gift for the President.
Klaatu is taken to an army hospital, where he is found to be physically human-like, but stuns the doctors with the quickness of his healing. Meanwhile the military attempts to enter Klaatu's ship, but finds it impregnable. Gort stands by, mute and unmoving.
Klaatu reveals to the President's secretary, Harley (Frank Conroy), that he bears a message so momentous and urgent that it can and must be revealed to all the world's leaders simultaneously. However Harley tells him that it would be impossible to get the squabbling world leaders to agree to meet. Klaatu wants to get to know the ordinary people. Harley forbids it and leaves Klaatu locked up under guard.
Klaatu escapes and lodges at a boarding house, assuming the alias "Mr. Carpenter". Among the residents are Helen Benson (Patricia Neal), a World War II widow, and her son Bobby (Billy Gray). At breakfast the next morning, during alarming radio reports, Klaatu takes in the unknowing fellow boarders' suspicions and speculations about the purpose of the alien's visit.
While Helen and her boyfriend Tom Stephens (Hugh Marlowe) go on a day trip, Klaatu babysits Bobby. The boy 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 visit the heavily guarded spaceship and the Lincoln Memorial. Klaatu, impressed by the Gettysburg Address inscription, queries Bobby for the greatest person living in the world. Bobby suggests a leading American scientist, Professor Jacob Barnhardt (Sam Jaffe), who lives in Washington, D.C. Bobby takes Klaatu to Barnhardt's home, but the professor is absent. Klaatu enters and adds a key mathematical equation to an advanced problem on the professor's blackboard, and then leaves his contact information with the suspicious housekeeper.
Later, government agents escort Klaatu to see Barnhardt. Klaatu introduces himself and warns the professor that the people of the other planets have become concerned for their own safety after human beings developed atomic power. Klaatu declares that if his message goes unheeded, "Planet Earth will be eliminated." Barnhardt agrees to arrange a meeting of scientists at Klaatu's ship and suggests that Klaatu give a demonstration of his power. Klaatu returns to his spaceship the next evening to implement the idea, unaware that Bobby has followed him.
Bobby tells the unbelieving Helen and Tom what has transpired, but not until Tom finds a diamond on the floor of Klaatu's room do they begin to accept his story. When Tom takes the diamond for appraisal, the jeweler informs him it is unlike any other on Earth.
Klaatu finds Helen at her workplace. She leads him to an unoccupied elevator which mysteriously stops at noon, trapping them together. Klaatu admits he is responsible, tells Helen his true identity, and asks for her help. A montage sequence shows that Klaatu has neutralized all electric power everywhere around the planet except in situations that would compromise human safety, such as hospitals and airplanes.
After the thirty-minute blackout ends, the manhunt for Klaatu intensifies and Tom informs authorities of his suspicions. Helen is very upset by Tom's betrayal of Klaatu and breaks off their relationship. Helen and Klaatu take a taxi to Barnhardt's home; en route, Klaatu instructs Helen that, should anything happen to him, she must tell Gort "Klaatu barada nikto". When they are spotted, Klaatu is shot by military personnel. Helen heads to the spaceship. Gort awakens and kills two guards before Helen can relay Klaatu's message. Gort gently deposits her in the spaceship, then goes to fetch Klaatu's corpse. Gort then revives Klaatu while the amazed Helen watches on. Klaatu explains that his revival is only temporary; even with their advanced technology, they cannot truly overcome death. 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 other inhabitants of the universe who have created and empowered a race of robot enforcers including Gort to deter such aggression. He warns that if the people of Earth threaten to extend their violence into space, the robots will destroy Earth, adding, "The decision rests with you." He enters the spaceship and departs.
The original story ends slightly differently. After helping the robot to revive Klaatu, a newsman asks it to be sure to tell its masters that Klaatu's death was an unfortunate accident. The robot responds, "You are mistaken. I am the master."