Murshed was born to his parents Syed Abdus Salek, a member of the Bengal Civil Service and Afzalunnessa Begum, the sister of Sher-e-Bangla A. K. Fazlul Huq.
Murshed obtained his bachelors in Economics from Presidency College, Calcutta in 1931, masters from Calcutta University in 1932, and L.L.B degree in 1933.