Sherman was born in Philadelphia, Pennsylvania to Julia (née Shapiro) and Joseph T. Sherman, an attorney. Sherman is an openly gay Jew and has lived in London since 1980. He attended the Boston University College of Fine Arts, and received a BFA in dramatic arts in 1960.

Sherman's most successful film was adapted from the original script Alive and Kicking/Indian Summer, which he authored himself. On Broadway and in the West End he is best known for Bent, which was nominated for a Tony Award in 1980. This play was the first to deal with the treatment of homosexuals by the Nazis during World War II. Set primarily in a concentration camp, it generated controversy for the two scenes in which gay inmates achieve climax through words. He also wrote the book for the musical The Boy from Oz, based on Peter Allen's life and career, earning him a second Tony nomination.

Sherman has written two collections of gay-themed plays. His play Rose was nominated for a Laurence Olivier Award for Best New Play in 2000. Olympia Dukakis starred in the Broadway production that same year.