Linda Hunt was born in Morristown, New Jersey, and raised in Westport, Connecticut. She is one of the two daughters of Raymond Davy Hunter, vice president of Harper Fuel Oil on Long Island, and Elsie Doying Hunter, a piano teacher who taught at the Westport School of Music and accompanied the Saugatuck Congregational Church choir. Hunt attended the Interlochen Arts Academy and the Goodman School of Drama in Chicago (now part of DePaul University).
Hunt's film debut in 1980 was in Robert Altman's musical comedy Popeye. Two years later, she co-starred as Billy Kwan in The Year of Living Dangerously, Peter Weir's film adaptation of the novel of the same name. For her role as the male Chinese-Australian photographer Billy Kwan, Hunt won the Academy Award for Best Supporting Actress in 1983, becoming the first person to win an Oscar for playing a character of the opposite sex. Hunt also played a nurse in She-Devil (1989), the austere school principal opposite Arnold Schwarzenegger in Kindergarten Cop in 1990, and the assassin Ilsa Grunt in If Looks Could Kill (1991).
Also a well-known stage actress, Hunt has received two Obie Awards and a Tony Award nomination for her theatre work. She created the role of Aunt Dan in Wallace Shawn's play Aunt Dan and Lemon. She portrayed Sister Aloysius in the Pasadena Playhouse production of John Patrick Shanley's play Doubt. She was praised for her performance as the title character in Bertolt Brecht's Mother Courage and Her Children. Hunt also appeared as Pope Joan in Caryl Churchill's Top Girls when London's Royal Court Theatre's production was staged at the Public Theater in New York.