"The writer died at 87 after a prolonged illness due to age-related problems at his residence in the city," family sources said.
The writer's family has decided to donate his body for medical research.
Mehta's columns, which first appeared in Gujarati weekly magazine 'Chitralekha' in 1971, were adapted into a TV serial, "Taarak Mehta Ka Ooltah Chashma" in 2008, making him a household name across the country.
Prime Minister Narendra Modi took to Twitter to pay his tributes to the writer in a series of tweets.
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Along with a photo taken with Mehta, the PM also said Mehta was a man who "never left the company of his pen and satire".
"Tributes to famous playwright and humourist Taarak Mehta. He spent a lifetime dedicated to satire and pen.
"I have had the good fortune of meeting Taarak Mehta. I had also met him when he was honoured with the Padma Shri award," he said.
Delhi Chief Minister Arvind Kejriwal also condoled the writer's demise.
"Gujarati writer and Padma Shree (sic) Tarak Mehta ji passes aways. May his soul rest in peace," he tweeted.
Gujarat Chief Minister Vijay Rupani remembered Mehta as a person "who always brought smile to our faces."
He tweeted, "Saddened by the death of Tarak Mehta - humorist and columnist. He always brought smile to our faces. My condolences to family members."
Senior state Congress leader Shaktisinh Gohil, who visited Mehta's residence to pay homage, said, "The beauty of the writings of Tarak Mehta was that it had nothing against anyone, nothing vulgar and not even a bad word, but it made us all laugh. The loss is very grave."
"His writing was a class apart. His writings did not have any vulgarity, but made generations laugh till pain in our stomaches," said actor Jitendra Thakkar, who has acted in many plays written by Mehta.
His death was also mourned by several film and television actors.
Bollywood actor Paresh Rawal tweeted, "Extremely saddened by the passing away of Shri Tarak Mehta... A great humorist in any language! RIP Mehta Saheb."
Actress Richa Chaddha said, "Rip Tarak Mehta. Thank you for the humour. You shall be missed."
"Saddened by the news of #TaarakMehta sir passing away. Last time when I met him, I could see his health failing him. He was still spirited... And full of life... My respect to him.