Devi's father and guru Alauddin Khan, founder of the "Senia Maihar gharana" or "Senia Maihar School" of Hindustani classical music, was a noted musician and guru of Indian classical music. Her uncles, Fakir Aftabuddin Khan and Ayet Ali Khan, were noted musicians at their native place Shibpur, in the present-day Bangladesh. Her brother Ali Akbar Khan was a legendary Sarod maestro and was considered a "national living treasure" in India and the USA. Her former husband, virtuoso Sitar maestro Ravi Shankar, was perhaps the most famous Indian classical musician internationally.
She married her student Rooshikumar Pandya in 1982. He was 13 years younger than her. He died in 2013.
Annapurna Devi became a very accomplished Surbahar player of the Maihar gharana (school) within a few years of starting to take music lessons from her father, and started guiding many of her father's disciples, Nikhil Banerjee and Bahadur Khan) in classical music as well as in the techniques and intricacies of instrumental performances. Meanwhile, Alauddin Khan's Sitar student Ravi Shankar married Annapurna. (There is no documentary evidence, saying on the basis of Pandit Jotin Bhattacharya's two vol. Bengali book, Ustad Allauddin Khan o Aamraa. The marriage took place because of the eagerness and proposal of Uday Shankar.). The marriage between Ravi Shankar and Annapurna Devi took place when Ravi was 21 years and Annapurna was only 14 years old. She converted to Hinduism upon marriage. The marriage lasted more than two decades, and she gave birth to a son, Shubhendra Shankar (1942–1992), whom Annapurna Devi trained in Sitar. Shubhendra Shankar (or "Subho", as he was popularly known) had rigorous training in Sitar under the tutelage of his mother. His father, however, chose to interrupt his musical talim or training and, instead brought him to the United States. Shubhendra died at an early age, after a marriage and the birth of three children. Shubhendra did not have a solo career in classical music, but did very occasionally accompany his illustrious father Ravi Shankar in concerts in the USA and abroad.
In the 1950s, both Ravi Shankar and Annapurna Devi performed duets in Delhi and Calcutta, principally at the college of her brother, Ali Akbar Khan. But later, Shankar started getting insecure since she used to be applauded in concerts more than he was and she thereafter decided not to perform publicly. Even the movie Abhimaan is believed to be based on the same scenario. Annapurna Devi was already a master of the Surbhahar when Ravi Shankar came to study with her father, Alauddin Khan, in the court of Maihar, India.
Though she refrained from taking music as her profession, she received utmost reverence in all circles of Indian classical music especially for her unending repertoire in Indian classical music, and her traditional "dhrupadi" approach to music. She has received some of the most distinguished musical and civilian honours of India. She is the recipient of, among many, the Padma Bhushan (India's third highest civilian honour) in 1977; and the Sangeet Natak Akademi Award (the highest Indian honour in performing arts) in 1991; and the Deshikottam which is an honorary doctorate degree by Nobel laureate poet Rabindranath Tagore's Visva-Bharati University in 1999. In the year 2004, the Sangeet Natak Akademi, the Government of India's highest organisation for promoting music and other fine arts, has appointed her a "Ratna" or jewel fellow (a lifetime honour).
She has not recorded any music albums. But some of her performances (notably, 1. Raga Kaushi Kanara and Raga Majh Khamaj, Surbahar recital; and 2. Raga Yaman duet Surbahar recital with Ravi Shankar) that have been secretly taped from her earlier (1950s) concerts, are non-commercially available among a percentage of music lovers in India.
In spite of her avoidance of media-limelight, she continues to be thought of as a classical instrumentalist of the highest calibre in India.