The movie opens with the invisible Nick Halloway (Chevy Chase) dictating his memoirs into a video camera. To prove it is not a camera trick, he chews some bubble gum. Nick narrates the story of how he came to be invisible, beginning a few days earlier at his job as a stock analyst. His secretary refers to him as a "bullshit artist", and he spends most of his life avoiding responsibility and connections with other people. At his favorite bar, the Academy Club, his friend George Talbot (Michael McKean) invites him to join his table where Nick meets Alice Monroe (Darryl Hannah). Sharing an instant attraction, Nick and Alice make out in the ladies room. When Alice has to leave, Nick drinks heavily to console himself, although the pair set a lunch date for Friday.
The following morning, Nick is unable to avoid going to a shareholder's meeting at Magnascopic Labaratories. Unable to endure the droning presentation by Dr. Bernard Wachs (Jim Norton), Nick leaves in search of a bathroom. When he asks a lab technician for directions, the technician spills his coffee onto a computer console. Nick eventually finds an empty sauna and lies down for a nap. Meanwhile, the coffee has caused a meltdown, and the entire building is evacuated. The building seems to explode, but there is no debris. Instead, much of the building is rendered invisible, including Nick.
CIA operative David Jenkins (Sam Neill) arrives on the scene to contain the damage, and he discovers Nick's condition. While they are transferring him to an ambulance, the agents joke about how Nick will spend the rest of his life hooked up to machines and being studied by scientists. In a panic, Nick flees. Jenkins convinces his supervisor Warren Singleton (Stephen Tobolowsky) not to notify CIA headquarters; so, that they can capture and take credit for Nick, who could become the greatest secret agent in the world.
Nick holes up in his apartment, but Jenkins tracks him down using the guest list for the meeting. Nick decides to hide at the Academy Club. He locates Dr. Wachs in the hope that he can restore Nick's visibility. Wachs has no idea how to help, however. After Nick runs, Jenkins arrives and interrogates Wachs and eventually kills him to keep Nick's invisibility a secret. After a confrontation at Jenkins' office, Nick decides to flee San Francisco to George's remote beach house. Unfortunately, George arrives with his wife, Alice and another friend to spend the weekend. Nick reveals his condition to Alice, who decides to help him.
The pair board a train for Mexico, where Nick wants to set up a new life, trading stocks through Alice as a proxy. Jenkins and his men track them down on the train, and during the ensuing confrontation, Nick falls off the train and into a river. He makes his way to the video store, where he tapes his memoirs.
At the end of the tape, he records an ultimatum for Jenkins: exchange Alice for the tape, or Nick will give it to the CIA. Jenkins agrees, putting Alice into a cab as his men surround Nick. However, Nick has disguised himself as the cab driver, and George is standing in for Nick in the exchange. Jenkins pursues the cab, eventually cornering Nick on top of a building. Nick tricks Jenkins into jumping off the building to his death.
In the final scene set months later, Nick and Alice are hiding out in Switzerland, and the film closes with shots of a still invisible Nick skiing down to their chalet, where a pregnant Alice greets him with a kiss.