Hecht was born in Princeton, New Jersey, the daughter of Lenore, a psychotherapist, and Richard Hecht, a physicist. When she was three, Jessica moved with her parents and her sister to Bloomfield, Connecticut. Following the divorce of her parents, her mother remarried when Jessica was twelve and her sister Elizabeth was fourteen. They were brought up by her mother and her step-father Howard Iger, a psychiatrist, who had custody of his children, Andrea, age five, and Russell, age three. Hecht attended Connecticut College and in 1987, Hecht graduated from the NYU Tisch School of the Arts, earning a Bachelor of Fine Arts in Drama.