Brilliant but timid and bankrupt scientist Reed Richards is convinced that all evolution is caused by clouds of cosmic energy. He calculates that Earth is going to pass one of these clouds soon, and together with his partner, the gentle yet gruff pilot Ben Grimm, pleads his MIT classmate, ultra-rich and arrogant Dr. Victor von Doom, CEO of his own enterprise, to let him onto his space station. Von Doom agrees, but only under the conditions that he has the final say in all the experiments and receives a majority of the profits. They also encounter the calm and rational Susan Storm, von Doom's right hand and genetic researcher, and her diametrically opposed brother Johnny, the maverick hot-headed playboy pilot. Susan attended MIT with Reed and Victor. She dated Reed at the time and there is obviously some tension between the three. Apparently, Susan left Reed because she wanted him to take action and not only see things in terms of variables.

The quintet travels to space to observe the cosmic energy clouds, but the clouds materialise well ahead of schedule, and all five are zapped by its vast energies. The astronauts make it home intact, but suddenly, they begin to mutate and develop their characteristic powers. Reed, Susan and Ben see them as a curse and Reed and Sue work on a healing chamber while the four room in Reed's high tech Baxter Building loft-turned-laboratory. Only Johnny seems to embrace his powers, which are pyrokinetic in nature, and clashes with Ben, who evidently drew the shortest straw, becoming a superstrong, yet unsightly, rock creature. His disfigurement causes his fiancee to leave him which makes Reed vow to help Ben devolve to his human state, but he later gains another girlfriend in the blind woman Alicia Masters, who recognizes his desirability beneath his rocky body. Reed has become stretchy and durable, while Sue can become invisible and create force fields, especially when emotionally troubled.

While Ben broods about his situation on the Brooklyn Bridge, he stops a man about to commit suicide by jumping off. However, Ben's appearance so frightens the would be jumper that he falls into the bridge's traffic, forcing Ben to jump down to save him by forcefully stopping a truck, inadvertently causing a chain reaction pile up on the bridge. Just as Ben's compatriots looking for him arrive at the bridge, the accident soon escalates as a fire breaks out in the wrecks while an arriving fire truck crashes and almost falls off the bridge, forcing the four to use their powers to prevent disaster. They are successful and the media throngs them and immediately uses Johnny's impromptu group name for themselves, The Fantastic Four. In a simialar manner, Johnny later chooses their codenames for them.

Doom is turning into organic metal capable of manipulating energy. After killing one of the board of directors of his company and his physician with his burgeoning energies, he sees the opportunity to finish off his rival Reed once and for all, blaming him for the recent failure of his company. He tricks Ben into turning on his friends, thinking that they were not working on a cure with due diligence. However, the machine is ready and Doom tricks Ben into using it and becoming normal again. Doom immediately attacks Ben and then renders Reed unconscious and takes him prisoner. After freezing him to prevent him using his stretch powers and torturing him in that state, Doom fires a missile towards Johnny who must use his powers to fly away to lead the missile to open water where he ignites a garbage scow to lure the missile away from himself. Susan realizes where Reed is and confronts Doom while Ben decides that he must become The Thing again to confront his enemy.

Eventually, Ben fights Doom on the street until the rest of the team joins him, sporting their specialized suits invented by Reed and likely based in part on the design of von Doom. Together under Reed's direction, the Fantastic Four vanquish their arch enemy with a coordinated attack that seemingly leaves Doom as a statue of inert metal.

In the end, the foursome decide to embrace their roles as superheroes and officially organize as the Fantastic Four with Reed proposing to Sue, and her accepting while Ben, with the help of Alicia, comes to terms with his condition. However, Doom's associate is transporting his employer's supposed dead body back to his homeland of Latveria (the country he ruled in the comics, where he could establish a real power base if he fully revives). Before the movie ends, evidence that Doom is still alive and well is presented.