Agha was born to Nasreen (born as Zarina Ghaznavi) and Liaqat Gul Tajik. Her father was given the title of Agha, as he was a reputed businessman of precious stones and antiques in Iran. Salma's maternal grandparents are actor Jugal Kishore Mehra and actress Anwari Begum who starred in the first ever made Heer Ranjha (1932). Salma's biological maternal grandfather was Rafiq Ghaznavi. Nasreen was later adopted by Jugul Kishore Mehra, who converted to Islam and took on the name Ahmed Salman.