Tucci was born in New York City, the daughter of Laura (née Rusconi 1911-1989) and Niccolò Tucci (1908-1999), a Writer. She has a brother, Vieri. Her parents came to America in 1938 to escape from World War II. She is married to Writer Robert Gottlieb. Her daughter Lizzie is a documentary filmmaker. Her film Today's Man featured her family and tells the story Tucci's son Nicky and his fight with Asperger syndrome. Tucci began studying acting at a young age, studying with Lee Strasberg and Joseph Papp. She briefly attended Barnard College.

Off-Broadway
Tucci began her career Off-Broadway. One of her earliest credits is a 1963 production of The Trojan Women. In 1986, she starred in a production of A Man for All Seasons as Alice More. Tucci played the role of Ruth Steiner in Collected Stories, in its 1997 New York debut. The play was nominated for the Pulitzer Prize for Drama. In 2014, she appeared in a production of Love and Information at the Minetta Lane Theatre. Regionally she has performed in many shows with the Long Wharf Theatre and the Williamstown Theatre Festival.

She was nominated for the Tony Award for Best Featured Actress in a Play in 1967 for her performance in The Rose Tattoo. She played Koula in the 2015 mini-series The Slap.

Tucci began appearing in film in 1969. Her first credits were in Robert Frank's Me and My Brother and a CBS Playhouse production titled Shadow Game. She played Lisa in Sidney Lumet's 1983 film Daniel. In Gus Van Sant's 1995 film To Die For she portrayed Angela Maretto.