The actor made a huge splash in 1973 with his first lead role in Bobby - a teenage love story.
He played the romantic lead in dozens of films for over two decades, after which he made a successful transition to character roles.
Rishi Kapoor debuted as a child actor in 1970 in his father Raj Kapoor's film, Mera Naam Joker.
His death comes a day after the passing away of Bollywood actor Irrfan Khan.
apoor was diagnosed with cancer in 2018 and returned to India last September after a year-long treatment in New York.
He was taken to hospital on Wednesday morning after he complained of breathing difficulties, his brother Randhir Kapoor told Press Trust of India.
Tributes have been pouring in for Kapoor from his fellow Bollywood actors and politicians.
Amitabh Bachchan who worked in several hit films with Kapoor tweeted: "He's GONE .. ! Rishi Kapoor .. gone .. just passed away .. I am destroyed !" This breaking news story is being updated and more details will be published shortly. Please refresh the page for the fullest version.