Shankar, who was the father of the American singer-songwriter Norah Jones, died in a hospital in San Diego where he was preparing to undergo surgery, according to Indian television news channels.
Indian Prime Minister Manmohan Singh expressed his sadness over the death and hailed Shankar as “a national treasure and global ambassador of India’s cultural heritage”.
“Mourn (the) passing of a musical genius and gentle soul,” Nirupama Menon Rao, the Indian ambassador to the United States, said on her Twitter feed.
Shankar, who was living in California when he died, was born into a high-caste Bengali Brahmin family in the Hindu holy city of Varanasi in northern India on April 7, 1920.
He taught close friend the late Beatle George Harrison to play the sitar and collaborated with him on several projects, including the groundbreaking concert for Bangladesh in 1971. The Beatles called him “The Godfather of World Music”.