Born in Mumbai, Kapoor is the second son of film director and star Raj Kapoor. He did his schooling with his brothers at Campion School,Mumbai. His brothers are well-known actors: Randhir Kapoor and Rajiv Kapoor. He is father of actor Ranbir Kapoor and designer Riddhima Kapoor Sahani. Rishi is the paternal uncle of today's actresses Karisma Kapoor and Kareena Kapoor. He is of Punjabi Hindu origin.