Ikramullah was born in London, England to an Indian Bengali family. Her father, Mohammed Ikramullah, later became the first Foreign Secretary of Pakistan and her mother, Shaista Suhrawardy Ikramullah, was one of the first Muslim women to become a politician and diplomat in the Indian Subcontinent. Her mother, who later served as a Delegate to the United Nations and an Ambassador to Morocco, was a member of the Suhrawardy family of Calcutta, India. She became a Mohajir by moving to West Pakistan, though many of her prominent relatives remained in India and others remained in what would become Bangladesh.