Shah died of a heart attack, a family member told PTI.
His last rites were performed at Shivaji Park crematorium here by daughter Shilpa with close family members and friends from the film fraternity in attendance.
"Jaane Bhi Do Yaaro" actors Naseeruddin Shah, Satish Shah and writer Sudhir Mishra came to pay tributes to the director at his residence and were also present at the crematorium.
Others who attended the funeral included celebrities such as Anil Kapoor, Inder Kumar, Deepak Dobriyal, Prahlad Kakkar, Ratna Pathak, Rakesh Bedi, Mita Vashisht, Raveena Tandon and Ashoke Pandit.
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The movie, featuring Naseeruddin Shah, Ravi Baswani, Om Puri, Pankaj Kapur, Satish Shah, Satish Kaushik, Bhakti Barve and Neena Gupta, went on to achieve cult status despite a poor box office showing.
More than three decades later, the film -- revolving around two bumbling photographers, a canny newspaper editor and corrupt civic officials -- continues to be relevant and a scathing commentary on contemporary India.
Shah received his first and only National Award - Indira Gandhi Award for Best First Film of a Director - for the film.
After "Jaane Bhi Do Yaaro", Shah switched to television and teamed up with Saeed Akhtar Mirza for his debut TV show "Nukkad".
One of the most popular shows in the '80s, "Nukkad" gave Indian audiences memorable characters like Khopdi, Kaderbhai and Ghanshu Bhikari.
His next TV show was "Wagle Ki Duniya", based on cartoonist R K Laxman's common man.
Shah came back to Bollywood in 1993 with the Shah Rukh Khan-starrer "Kabhi Haan Kabhi Naa". The film received critical acclaim and is counted among Shah Rukh's best performances.
It was a box office success and became one of the highest grossing films of 2000. The film helped establish Preity Zinta's career in the Hindi film industry.
The director made a number of films after "Kya Kehna", but sadly commercial success eluded him.
Shah's sudden demise shocked his friends in the industry.
His friend and colleague Satish Shah, who played one of the principal characters in "Jaane Bhi Do Yaaro", told PTI, "I just got to know about Shah's demise. I have reached his house. It is really sad."
"'Jaane Bhi Do Yaaro' RIP Kundan Shah. Sad news," he wrote.
Filmmaker Mahesh Bhatt remembered Shah as a brave man "who added vigour to the alternate cinema stream with movies like 'Jaane bhi do yaaro'".
Farhan Akhtar wrote, "Saddened to learn that Kundan Shah is no more. Will never forget his genuineness, his cinematic knowledge and his unique sense of humour. RIP".
Karan Johar said, "RIP Kundan Shah... A cult filmmaker ... A solid story teller."
Sudhir Mishra said the director was a huge influence when he was a 22-year-old and helped him find his voice.
Riteish Deshmukh said, "RIP Kundan Shah.... A master storyteller no more. Condolences to the family and loved ones.
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