The United States and the Soviet Union have both developed technology that can miniaturize matter by shrinking individual atoms, but only for one hour. (The novel stated that the duration of miniaturization is inversely proportional to its degree. A 50% reduction, say, could be maintained for many days, but a reduction to microbial size could last for only an hour.)
Scientist Dr. Jan Benes (Jean Del Val), working behind the Iron Curtain, has figured out how to make the process work indefinitely. With the help of American intelligence agents, including agent Charles Grant (Boyd), he escapes to the West, but an attempted assassination leaves him comatose with a blood clot in his brain that no surgery can remove from the outside.
To save his life, agent Grant, Navy pilot Captain Bill Owens (Redfield), Dr. Michaels (Pleasence), surgeon Dr. Peter Duval (Kennedy), and his assistant Cora Peterson (Welch) are placed aboard a Navy submarine (originally designed to study the deep-sea spawning habits of fish) at the Combined Miniature Deterrent Forces facilities. The submarine, named Proteus, is then miniaturized to "about the size of a microbe", and injected into Benes. The team has 60 minutes to get to and remove the clot; after this, Proteus and its crew will begin to revert to their normal size, become vulnerable to Benes's immune system, and (in the words of Asimov's novelization) "kill Benes regardless of the success of the surgery."
The crew faces many obstacles during the mission. An arteriovenous fistula forces them to detour through the heart, where cardiac arrest must be induced (at the risk of killing Benes) to, at best, reduce turbulence that would be strong enough to destroy Proteus. After an unexplained loss of oxygen, they must replenish their supply in the lungs. They are forced to pass through the inner ear, requiring all outside personnel to make no noise, so as to prevent destructive shocks (a sound is accidentally made from a fallen surgery tool though, and the ship and crew are badly thrown about and Cora is, as a result, almost killed by antibodies). To top it all, they discover after their detour through the heart, the surgical laser that is needed to destroy the clot was damaged from the turbulence, as this was due to it not being strapped down as it was before. It is after learning what happened to the laser, the crew confirms a saboteur is on the mission. They must cannibalize their wireless radio to repair the laser, making communication and guidance from outside impossible to get from then on (although the surgeons outside Benes's body would still be able to track their every move). By the time they finally reach the clot, they have only six minutes remaining to operate and then exit the body.
Before the mission, Grant had been briefed that Duval was the prime suspect as a potential surgical assassin, but as the mission progresses, he pieces the evidence together, and near the end, instead begins to suspect Michaels. During the critical phase of the operation, Dr. Michaels knocks out Owens and takes control of Proteus, while the rest of the crew is outside for the operation. Duval successfully removes the clot with the laser, but Michaels tries to crash the submarine into the clot area to kill Benes. Grant fires the laser at the ship, causing it to veer away and crash. Grant saves Owens from the Proteus, but Michaels is trapped in the wreckage and killed when a white blood cell attacks, destroys and eats the ship. The remaining crew swim desperately to one of Benes' eyes, and thanks to General Carter (Edmond O'Brien) and Colonel Reid (Arthur O'Connell) figuring out their escape strategy shortly after the timer runs out, escape through a tear duct before returning to normal size