"Karnad died at his home at around 8.30 a.m. due to age-related symptoms," an official in the Karnataka Chief Minister's office told .
The veteran artist is survived by his widow Saraswathy Ganapathy, his son Raghu Amay and daughter Shalmali Radha.
As per Karnad's last wishes, his mortal remains were cremated at a local crematorium "quietly" in the presence of his family members, close relatives and a few friends. No rituals were conducted or customs observed.
The body was taken in an ambulance to Kalapalli electric crematorium in the city's eastern suburb, with his bereaved family, relatives and friends following it in a convoy without fanfare, police security or escort.
"Though the Karnataka government decided to conduct Karnad's last rites with state honours, we have decided to respect his wishes and allowed his family to do it accordingly," an official told .
When hundreds turned up at Karnad's house to pay homage, the family requested them to pay their last respects to him at the crematorium and declined to keep his body for public viewing outside.
According to a family source, Karnad succumbed to multi-organ failure at his residence on Lavelle Road, the city's upscale locality near Cubbon Park.
The state government declared a day's holiday on Monday as a mark of respect to Karnad and a three-day mourning will be observed across the state till June 12.
"The scheduled state Cabinet expansion on Wednesday has also been postponed to June 14 due to the mourning period," said the official in the chief minister's office.
President Ram Nath Kovind, Prime Minister Narendra Modi, Karnataka Chief Minister H.D. Kumaraswamy, former Prime Minister and Janata Dal-Secular supremo H.D. Deve Gowda and Union Minister for Chemicals and Fertilisers D.V. Sadananda Gowda have mourned Karnad's demise and offered their condolences to his family members and relatives.
"Girish Karnad will be remembered for his versatile acting across all mediums. He also spoke passionately on causes dear to him. His works will continue being popular in the years to come. Saddened by his demise. May his soul rest in peace," tweeted Modi.
In addition to the Jnanpith Award in 1988, he was also honoured with the Padma Shri and the Padma Bhushan, apart from four National Film Awards and a Sahitya Akademi honour.
Karnad was also a reputed scholar who raised his voice on socio-political issues.
In a career spanning six decades, Karnad acted in Kannada, Hindi and Marathi films, in both mainstream and parallel cinema. He also featured in television serials, including the famous 'Malgudi Days', based on the works of renowned Indian English author, R.K. Narayan.
He also bagged four Filmfare awards, including three for best director for "Vamsha Vriksha" in 1972, "Kaadu" in 1974 and "Ondanondu Kaladalli" in 1978 and one for best screenplay for "Gadhuli" in 1980 along with another noted Kannada film director B.V. Karanth.
Karnad, who straddled the worlds of theatre and cinema in various languages, was born on May 19, 1938 in Matheran. He graduated from the Karnataka University, and was a Rhodes Scholar in the University of Oxford, where he studied philosophy, politics and economics.
For television audiences, Karnad may be best remembered as Swami's father in the much-loved 'Malgudi Days' or as the presenter of Doordarshan's science show "Turning Point", while for Hindi movie audiences, his roles in "Manthan", "Nishant", "Pukar", "Iqbal", "Dor" and "Ek Tha Tiger" left an impact.
Karnad also served as director of the state-run Film and Television Institute of India (1974-1975) at Pune and was Chairman of Sangeet Natak Akademi and National Academy of the Performing Arts (1988-93).
The multi-faceted author and playwright hosted a weekly science programme on state-run Doordarshan titled "Turning Point".
Featuring scientist Yash Pal, the award-winning show explained complex, modern scientific discoveries in simple language.
( With inputs from IANS )