The premise has an important scientist defecting from the 'other side'. He suffers a brain injury in an assassination attempt. A team of doctors, plus a security-minded everyman, is placed in a submarine and shrunken to microscopic size. They are injected into the patient, and journey through the bloodstream to perform the surgery that will save his life.
Of course it isn't that easy. The crew includes a lunatic traitor, whom you will easily spot early on. The drama is increased by time constraints: the submarine and its crew can be shrunk for only sixty minutes (not 59, not 61). The heart can be stopped for just sixty seconds (not 61). When the crew reaches the inner ear, the operating room must be held in complete silence.
The plot holes are only too obvious. Reducing the size of the crew should not reduce their mass. If their mass was proportionally reduced, the loss of brain cells would render them mindless. If the crew automatically returns to full size in an hour, that would included the saline solution and the air in the sub, as well as the submarine itself. Surely the interior of the body is not lit up like an amusement park at night.
Such criticism would lose its edge if the script were a little better. The cast is filled with famous (but stiff) middle-aged actors (Stephen Boyd, Edmond O'Brien, Arthur Kennedy, Arthur O'Connell) who often wax philosophic about the body electric. Yet it was the billed player least known at the time, Raquel Welch, who would be become the most famous among the cast. Very early in her career, her celebrity as a sex symbol was established with her cavewoman outfit in One Million Years B.C..
Noted science fiction author Isaac Asimov wrote the novelization, which plugged some of the plot holes. What it lacked, besides Welch, was the film's expensive sets and special effects. Suspension of belief is still required, but the weird tinted lighting, lava lamp fluids, and extensive modern art sculptures at least create an impressive landscape.
Hollywood was also impressed. Fantastic Voyage won two Oscars (color sets, visual effects) and was nominated for three others (color cinematography, sound effects, film editing). Yet the film is probably better remembered today for a scene in which has the crew grabbing at Welch, whose skintight wetsuit had become covered with feisty antibodies.