He was born in Hereford, England to French parents a Jewish father and Catholic mother, both of Polish descent. Oz moved to California, United States with his parents when he was five years old.

Frank Oz is best known for his work as a puppeteer, performing with Jim Henson's Muppets. His characters have included Miss Piggy, Fozzie Bear, and Sam the Eagle on The Muppet Show, and Grover, Cookie Monster, and Bert on Sesame Street, among many others. In addition to performing a variety of characters, Oz has been one of the primary collaborators responsible for the development of the Muppets over the last 30 years. Oz has performed as a Muppeteer in over 75 movies, video releases, and TV specials, as well as countless other public appearances, episodes of Sesame Street, and other Jim Henson series. His puppetry work spans from 1969 to the present day.

Possibly Oz's most famous character is the diminutive Jedi Master Yoda from George Lucas' Star Wars series. Oz performed the voice and puppet (where applicable) for Yoda in Star Wars films between 1980 and 2005. Yoda first appeared in 1980's The Empire Strikes Back. Oz had a great deal of creative input on the character, and was himself responsible for creating the character's trademark style of reversed grammar.

As an actor, Oz appeared in 1980 as a corrections officer in The Blues Brothers movie, directed by John Landis. He also appeared in later Landis movies An American Werewolf in London, Spies Like Us, and Trading Places. In 1998, Oz portrayed a warden in Blues Brothers 2000. And while it wasn't for Landis, in 2001 he had a minor part in the Pixar film Monsters, Inc. as Randall's scare assistant Fungus.

Oz began his behind-the-camera work when he co-directed the fantasy film The Dark Crystal with long-time collaborator Jim Henson. The film featured the most advanced puppets ever created for a movie. Oz further employed those skills in directing 1986's Little Shop Of Horrors. The musical film starred Rick Moranis and Ellen Greene, as well as Steve Martin, Bill Murray, John Candy, Christopher Guest, and a 15-foot-tall talking plant (voiced by Levi Stubbs) which at times required up to 30 puppeteers to operate.

Oz went on to direct Dirty Rotten Scoundrels in 1988, starring Steve Martin and Michael Caine, What About Bob? in 1991, starring Bill Murray and Richard Dreyfuss, and HouseSitter in 1992. Later films include The Indian in the Cupboard (1995), In & Out (1997), Bowfinger (1999), The Score (2001), and the 2004 re-make of The Stepford Wives.

After Jim Henson's death, Frank put a reference to Jim in every movie he directs. He sees it as a tribute to Jim as well as a "thank you" to him for making Frank a star.