Born on 9 October 1945 as Masoom Ali Khan, the youngest of seven children, to Gwalior court musician Hafiz Ali Khan and Rahat Jahan. His family is part of the Bangash lineage and Khan is in the sixth generation of musicians; his family claims to have invented the "sarod". His personal name was changed by a sadhu to Amjad. Khan received homeschooling and studied music under his father. In 1957, a cultural organization in Delhi appointed Hafiz Ali Khan as its guest and the family moved to Delhi. Hafiz Ali Khan received training from the descendants of Tansen, the magical musician, was one of the 'Nav-ratna' ( nine gems) at the court of the Mughal Emperor Akbar. Thus, Amjad belongs to the lineage of Tansen. Friends of Hafiz Ali Khan convinced him of the importance of formal schooling for his son; as a result, Amjad was taken to meet the Principal of Modern School in New Delhi and admitted there as a day scholar. He attended Modern School from 1958 to 1963.