Salahuddin was born on 7 July 1937 in Jairajpur, Azamgarh, Uttar Pradesh. His father, Fazlul Bari, was a teacher at the Shibli National College, Azamgarh where he received his early education, and he later completed his undergraduate and master's degrees in 1955 and 1957 in chemistry from the Aligarh Muslim University. Initially as a research student, he took interest in physical chemistry, obtaining his PhD degree in chemistry from Aligarh Muslim University Aligarh (1962).