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.