"An era has passed away with Pandit Ravi Shankar. The nation joins me to pay tributes to his unsurpassable genius, his art and his humility," the Prime Minister said in his message.
Singh said that Ravi Shankar was "a national treasure and global ambassador of India's cultural heritage."
In her message, Lok Sabha Speaker Meira Kumar said India has lost a distinguished son.
The sitar icon's health had been fragile for the past several years and on Thursday he underwent a surgery at the Scripps Memorial Hospital in La Jolla, California where he breathed his last. He was 92.
