Dutt had been ill for some time and suffered a heart attack in Bombay Wednesday, the BBC reported.
Dutt, who represented Bombay in Parliament since 1984, was the minister of sport and youth affairs in the Congress Party-led Indian government.
Congress Party President Sonia Gandhi said Dutt was "a very special human being."
"He had friends and admirers -- not just in India but also across the world -- who will now miss him," Gandhi told the BBC.
Dutt, born in an area now part of Pakistan, began his acting career in the 1950s.
He gained international fame and an Oscar nomination for Best Foreign Film with "Mother India."
His last movie was the 2004 "Munnabhai MBBS," in which Dutt starred with his son, Sunjay.
In addition to Sunjay, he is survived by two daughters.