Sawant was born as Neeru to Jaya Bagdi, who married Sawant, a police constable at Worli Police Station, and named her children Sawant.[4] Sawant attended Goklibai High School in the Vile Parle suburb of Mumbai and later studied at Mithibai College. She is the sister of film director Rakesh Sawant and former actress Usha Sawant.