The Padma Bhushan awardee had been suffering from respiratory problems for the past few days, a family member said. He is survived by wife and two sons.
West Bengal Chief Minister Mamata Banerjee said his death has created a void in the field of classical music.
"My heartfelt condolences to his family and disciples," she said in a tweet.
The musician, born in 1933 at his maternal home in Bhagalpur, Bihar, learnt sarod under the tutelage of Pt Radhikamohan Moitra. His father, Prafulla Mohan Dasgupta, was a district magistrate and a music aficionado.
Dasgupta's body is kept at the Peace Haven morgue for people to pay their last respects. He will be cremated on Wednesday after his younger son returns from the US, one of his close disciples said.