Hossain was born in Dhoom, Bengal Presidency, British India (nowMirsharai Upazila, Chittagong, Bangladesh). His father, S. Rahman was a Member of the Provincial Assembly (MPA) of Pakistan (1960s) and a businessman. S. Rahman started his business in Kolkata in 1944 and moved to Chittagong after the Partition of Bengal in 1947. In Chittagong he founded Orient Builders Corporation, an infrastructure development company and Hotel Sayeman in Cox's Bazar in 1964. Mosharraf's mother, Panjubunnesa was a social worker and a devotee to women's education. She established the Panjubunnesa Girls' School in Goloker Hut.