Hedaya was born in Brooklyn, New York, to a Sephardic Jewish family from Syria. His father immigrated from Aleppo. Hedaya was raised in Bensonhurst, and worked as a junior high school teacher for many years before deciding to pursue acting full-time.

Alongside a successful career in the movies, Hedaya has held several TV roles, including Carla Tortelli's ex-husband Nick on the sitcom Cheers and its short-lived spinoff The Tortellis. He played the estranged father of Mallory Keaton's boyfriend, Nick, on the sitcom Family Ties. More recently, he played an Italian-American priest in the controversial and quickly cancelled NBC series The Book of Daniel. Adding to his list of television credits is his performance as the long-lost father of Adrian Monk on Monk. He also guest starred in 1997 and 2005 as a wise cracking lawyer on the medical drama ER.

In films, Hedaya has played the evil dictator Arius in 1985's Commando, Mel Horowitz, the father of Alicia Silverstone's Cher in the 1995 film Clueless. He played Julian Marty in the first Coen brothers' feature, Blood Simple. His physical similarity to Richard Nixon led to his being cast as the former president for the film Dick.

In 2006, Hedaya received the P.T. Barnum Award from Tufts University for his exceptional work in the field of media and entertainment.