Bhabha was born in Bombay, India in 1951, the daughter of Jewish refugee parents who had moved to India to flee Nazi Germany. The family moved to Milan Italy in 1961 when she was ten years old.

Bhabha matriculated at Bedales, a British boarding school. Bhabha received a first class honours degree in philosophy from Oxford University in 1973, and an M.Sc. in applied social studies in 1975 from Oxford. She received her law degree from the College of Law in London.

She is married to Homi K. Bhabha, the critical theorist. They have three children; Ishan, Satya, and Leah.