A denizen (Garry Shandling) of a faraway planet occupied only by highly evolved males is ordered by his superior, Graydon (Ben Kingsley), to find a female human, impregnate her and bring the baby back to the planet.
The visitor to Earth ends up in Phoenix, Arizona, where he assumes the name Harold Anderson and takes a job in a bank. There he meets a womanizing co-worker Perry Gordon (Greg Kinnear), who goes to Alcoholics Anonymous meetings strictly to meet women. Harold accompanies him to one and meets Susan (Annette Bening), a recovering alcoholic.
He must marry her before he can try to mate. After their wedding in Las Vegas, Susan finds herself wildly satisfied by Harold, even though men from his planet have no genitals and he has been equipped for his Earth visit with a penis that makes a loud whirring sound whenever he gets an erection.
Harold and Susan have a difficult time conceiving a baby. Meanwhile, Roland Jones (John Goodman), an employee of the FAA who learned of Harold’s odd behavior on an airplane, has become obsessed with proving him to be an alien and being the first one to find him.
When the child is born, Harold, following orders, abandons his wife and returns to his planet, but his sadness over hurting Susan leaves him with guilt and second thoughts even though people from his world theoretically have no emotions, so against the wishes of Graydon, he returns the baby to Susan and tells her the truth. Susan is angry, grateful, and completely disbelieving. Harold offers to prove that he is in fact an alien and does so just as Roland arrives, viewing Harold’s “act of proof” through the window. Instead of forgiving him and welcoming him back into their relationship, Susan breaks down in tears, saying, “I thought I had things right but then I married an alien!” Harold leaves.
Once outside, Harold sees Roland, who is delighted to know he was right all along about Harold being an alien. Roland implores Harold to come with him and admit this to his wife, who doesn’t believe him about Harold. Harold charitably agrees, but before that can happen, Graydon shows up with a phaser. Holding Harold at gunpoint, he declares he’s taking Harold back. Roland pulls his gun on the leader, who brags, “none of your primitive weapons can hurt me, and I can heal instantly from anything,” and shoots him in the chest. Graydon falls dead into the fountain.
Susan comes outside and says she thinks they should try to patch things up after all. Roland happily walks off with Graydon’s alien body. Susan and Harold retake their vows in the wedding she says she always wanted. On the drive home, he tells her that the citizens of his planet want him to take over as leader. They discuss it, but she doesn’t want to move since all her friends are here, and she knows nothing about the school system there. Harold grudgingly agrees to make the very long commute.