Kapur was born in Mumbai on 16 November 1985 to a Punjabi Hindu father Kumud Roy Kapur, and a Jewish mother Salome Aaron. His grandfather, Raghupat Roy Kapur, was a film producer in the early 1940s. Kapur is the youngest of the three siblings; his eldest brother, Siddharth Roy Kapur, was the chief executive officer of UTV Motion Pictures and is married to the actress, Vidya Balan. His second elder brother, Kunaal Roy Kapur, is also an actor.