Razzaq was born into a middle-class business family in South Damudya village under Damudya Upazila of Shariatpur District in the province of Bengal (now Bangladesh) to father Alhaj Imamuddin and mother Begum Akfatun Nesa. His childhood dream was to develop his village into an ideal village where everyone would prosper and be solvent.

Razzaq passed his Secondary School Certificate examination from Damudya Muslim High School in 1958 and his Higher Secondary School Certificate examination from Dhaka College in 1960, he then enrolled at the University of Dhaka and passed the BA (Honors) in political science and in 1964 he enrolled and passed the MA in political science. Later he passed LLB and enrolled as a lawyer in 1973.

Razzaq married Farida Razzaq in 1973 and is the father of Nahim Razzaq and Fahim Razzaq