The Press Trust of India said Puri had died of a heart attack at his residence in Mumbai, the home of Bollywood.
Puri made his film debut in a Marathi-language movie in the mid 1970s before going on to star in a number of major Hindi hits as well as, controversially, in some Pakistani movies.
He also appeared in a number of British films, most notably Richard Attenborough's 1982 epic on the life of India's independence movement leader Mahatma Gandhi. He also appeared in Hollywood film "Charlie Wilson's War".
Puri starred opposite legendary British actress Helen Mirren in the 2014 film "The Hundred Foot Journey".
Tributes poured in from the world of Bollywood as actors and directors woke to the news of his death.
"Seeing him lying on his bed looking so calm can't believe that one of our greatest actors #OmPuri is no more. Deeply saddened & shocked," tweeted actor Anupam Kher.
"The Prime Minister condoles the passing away of actor Om Puri & recalls his long career in theatre & films," read a tweet on Indian leader Narendra Modi's official Twitter account.
Puri was born in Haryana state to a Punjabi family in 1950.