Shankar, a three-time Grammy winner with legendary appearances at the 1967 Monterey Festival and at Woodstock, had been in fragile health for several years and had surgery on Thursday.
Indian prime minister Manmohan Singh called Shankar a “national treasure and global ambassador of India’s cultural heritage”.
“An era has passed away with Ravi Shankar,” he said. “The nation joins me to pay tributes to his unsurpassable genius, his art and his humility.”
Shankar’s daughters, Norah Jones and Anoushka Shankar, are acclaimed musicians. He is also survived by a son, three grandchildren, and four great-grandchildren.
Shankar is credited with popularising Indian music through his work with The Beatles in the late 1960s.
Setting up before the 1971 Concert for Bangladesh, Shankar was surprised to be applauded by the audience. “If you like our tuning so much, I hope you will enjoy the playing more,” he told the confused crowd.