Yusufi was born in a learned family of Jaipur, Rajasthan, on 4 September 1923. From his paternal side he was Pashtun of the Yusufzai clan, while from his maternal side he was a Rajput of the Rathore clan. His father Abdul Karim Khan Yusufi was chairman of the Jaipur Municipality, and later Speaker of the Jaipur Legislative Assembly. Yusufi completed his early education in Rajputana and earned BA from Agra University while MA Philosophy and LL.B from Aligarh Muslim University. After the partition of India and formation of Pakistan, his family migrated to Karachi, Pakistan.