The singer died of multiple organ failure at the Breach Candy Hospital in Mumbai after she was admitted on 11 January with COVID-19
Born in 1929 in pre-independence India, Mangeshkar's career spanned eight decades - from the era of Frank Sinatra to Adele - having begun singing on stage aged just nine.
At 13 she acted in a Marathi film and also had some small roles in Hindi cinema, but singing was her passion.
She went on to perform an estimated 15,000 songs in more than a dozen languages and was considered the voice of Bollywood, working with nearly every director, actor and actress in the industry.
Fondly revered as the "Melody Queen" and "Nightingale of India", she enthralled listeners with her lilting voice and range, singing everything from patriotic songs to romantic numbers, both in films and albums.
The country's president Ram Nath Kovind has described her death as "heart breaking".
Two days of national mourning will be observed with the national flag will flying at half mast, according to government sources.
Mangeshkar, the eldest of five children, never married.
She is survived by her four siblings, who are all accomplished singers and musicians.