Zeba is the daughter of Yahya Bakhtiar, a lawyer, politician and pre-independence Muslim League activist who served as the Attorney General of Pakistan, and also played a key role in framing Pakistan's current constitution. Her father belonged to Quetta, while her mother Eva Bakhtiar was an English woman born to Hungarian parents. Her father died in 2003, and her mother died in 2011. Her parents met in the UK in the early 1940s and married, with her mother eventually settling in Pakistan in 1949 after graduating from the University College London. Zeba has two brothers, Salim and Karim, who are both doctors, and a sister, Saira. She was raised in Quetta, and moved to Karachi later.