The film opens with an Om mother fleeing with her baby before she is killed when young Draags toy with her. The orphan is found by Tiwa, daughter of the high-ranking Master Sinh, who keeps him as a pet and names him Terr. Because Draag lessons come through a headset and Terr stays close to Tiwa, he secretly absorbs Draag knowledge, including their language and science.
As Tiwa grows up and turns to Draag meditation, Terr escapes, taking the learning headset with him. He finds the wild Oms living in the parks. After initial distrust, the headset spreads literacy and technical skill among them. The Draags then launch a de-Oming campaign, and many Oms are killed. The survivors flee to an abandoned rocket depot and prepare for resistance.
The key revelation concerns Draag meditation. In it, Draags travel in spirit to the Fantastic Planet, a moon where their minds join headless statues and mate with beings of other species. This is how the Draags reproduce and survive. The Oms fly rockets to the moon and begin destroying the statues, which threatens the Draag species itself.
Facing their own extinction, the Draags agree to peace. The Oms get their own artificial satellite, which they name Terr, and the two species coexist. The hidden meaning becomes clear only at the end: the all-powerful oppressor had a fatal dependency the oppressed could exploit once they had enough knowledge. Liberation came from understanding, not strength.