She was 92.
She was declared dead at 3.51 am, hospital officials said.
She was a recipient of the Padma Bhushan award.
'Ma', as she was popularly addressed, was born in Madhya Pradesh's Maihar town to Ustad 'Baba' Allauddin Khan and Madina Begum. She was the youngest of four children, the spokesperson said.
World renowned maestro, Ustad Ali Akbar Khan, was her sibling, the spokesperson added.
Annapurna Devi was a disciple of her father whose inestimable contribution to Indian music resulted in the Senia-Maihar gharana. Her training started early when she was around five years old and she graduated from the sitar to her chosen instrument, the surbahar.
She remained a recluse for most of her life. Much of her time was dedicated to teaching a small but select group of students.
She was married to sitar maestro Pandit Ravi Shankar and had a son, Shubhendra 'Shubho' Shankar, who passed away in 1992.
In 1982, she married Rooshikumar Pandya, a management consultant. Pandya passed away in 2013.
Her students include Aashish Khan (sarod), Amit Bhattacharya (sarod), Bahadur Khan (sarod), Basant Kabra (sarod), Hariprasad Chaurasia (bansuri), Jotin Bhattacharya (sarod), Nikhil Banerjee (sitar), Nityanand Haldipur (bansuri), Peter Klatt (sitar), Pradeep Barot (sarod), Sandhya Phadke (sitar), Saswatti Saha (sitar), Sudhir Phadke (sitar), Suresh Vyas (sarod), the spokesperson said.