Dutt was the minister of sports and youth affairs in India's Congress-led government and represented Mumbai, formerly known as Bombay, in parliament.
Dutt had been sick with a high fever for four days before the heart attack, said D. Suresh, one of his employees.
"He was admitted to the hospital last week. He has not been keeping very well for quite some time. He passed away this morning," Congress party colleague K Bastiwala told AFP.
Fans crowded outside Dutt's home in suburban Mumbai minutes after news of his death was flashed on television.
Dutt was a popular politician and one of the first actors from Mumbai's huge movie industry to enter politics.
Dutt contested elections to India's lower house of parliament for the first time in 1984 after joining the Congress party.
He was elected five times as a member of parliament from his local Mumbai constituency, Bandra.
He was a major Bollywood star in the 1950s and 1960s and was best known for his role in the film, Mother India.
He was married to Nargis, a popular Indian actress who died in 1981. He is survived by two daughters and son Sanjay Dutt, who is also a leading Bollywood actor.