Sanjay Dutt was born in Bombay (now Mumbai since 1995), Bombay State, to parents who were noted Hindi cinema actors Sunil Dutt and Nargis Dutt. Born to a Punjabi Hindu (Mohyal Brahmin) father and a Muslim mother of Punjabi descent, Dutt's ancestry can be traced back to the Rawalpindi Division of West Punjab (present-day Pakistan); with his paternal village being Khurd in Jhelum District. Through his father, he belongs to the Hussaini Brahmin community, which reveres Imam Hussain and has participated in the battle of Karbala, the community's fluid identity as half-Hindu and half-Muslim having made it vulnerable during the 1947 Partition riots. Sanjay has two sisters, Priya Dutt and Namrata Dutt. He is the maternal grandson of music composer Jaddanbai and nephew of actor Anwar Hussain.
Sanjay's name was chosen by crowdsourcing via the Urdu language film magazine Shama. His mother died in 1981, shortly before his debut film's premiere; her death is cited as the instigator of his drug abuse. Dutt made his acting debut at an early age, playing a Qawali singer in his father's film Reshma Aur Shera (1971).