The sitar player - a three-time Grammy winner - passed away following heart valve surgery, his family and record label have confirmed.
"It is with great sadness that the Ravi Shankar Foundation and East Meets West Music report the death of maestro Ravi Shankar on December 11, 2012, near his home in southern California," read a statement issued on Tuesday evening.
"[He] had suffered from upper-respiratory and heart issues over the past year, and underwent heart valve replacement surgery last Thursday (December 6). Though the surgery was successful, recovery proved too difficult."
Born on April 7, 1920 in Varanasi, Shankar began to tour Europe and America during the 1950s. He was credited with popularising Indian classical music among international audiences.
Shankar taught George Harrison of The Beatles how to play the sitar, and the pair collaborated on numerous occasions, becoming firm friends. He also worked with members of the classical music community, including Yehudi Menuhin and Philip Glass.
He was honoured with India's highest civilian accolade, the Bharat Ratna, in 1999, and was nominated to the Indian upper house of parliament in 1986 for a six-year term.
Shankar also received an Academy Award nomination with George Fenton for 'Best Original Score' in 1983, recognising the pair's work on Richard Attenborough's Gandhi.
In 1998, he was honoured with the prestigious Polar Music Prize alongside Ray Charles. The award is presented annually by the Stig Anderson Music Award Foundation, in recognition of exceptional contributions to and achievements in music.
His final album Living Room Sessions - Part 1 is in contention at the forthcoming 55th Grammy Awards, and he performed his final concert on November 4 in Long Beach, California.
Shankar is survived by his wife Sukanya, daughters Norah Jones and Anoushka Shankar Wright, plus three grandchildren and four great-grandchildren.
Sukanya Shankar and Anoushka Shankar Wright's statement in full:
"It is with heavy hearts we write to inform you that Pandit Ravi Shankar, husband, father, and musical soul, passed away today, December 11, 2012.
"As you all know, his health has been fragile for the past several years, and on Thursday he underwent a surgery that could have potentially given him a new lease of life.
"Unfortunately, despite the best efforts of the surgeons and doctors taking care of him, his body was not able to withstand the strain of the surgery. We were at his side when he passed away.
"We know that you all feel our loss with us, and we thank you for all of your prayers and good wishes through this difficult time. Although it is a time for sorrow and sadness, it is also a time for all of us to give thanks and to be grateful that we were able to have him as a part of our lives.
"His spirit and his legacy will live on forever in our hearts and in his music."
Watch a clip of Ravi Shankar on The Dick Cavett Show below: