Jaffrey worked at All India Radio before emigrating to the United States on a Fulbright scholarship. He studied drama at Catholic University and later toured around the country performing Shakespearean plays.
In the 1980s, he had a successful career in Bollywood. Later, he went on to star in internationally successful movies, including Gandhi and A Passage to India, opposite such stars as Sean Connery, Michael Caine and Daniel Day-Lewis.
He was the first Indian recipient of the Order of the British Empire for his contributions to drama.
Jaffrey is survived by three children from his marriage to Indian actress Madhur Jaffrey. They were divorced in 1965.