Born Blanche Garfein in New York City, she is the daughter of Actress Carroll Baker and Director Jack Garfein. Her father is a Czech Jew, who survived the Holocaust; and her mother converted to Judaism. She also has a younger brother, Herschel Garfein. She spent her early life in Italy, where her mother had established a film career after leaving Hollywood in the mid-1960s. Baker attended Wellesley College from 1974 to 1976, and later studied acting at the Herbert Berghof Studio, the Lee Strasberg Theatre Institute, and the American School in London.