Mika Singh will now replace him on the show.
The 38-year-old singer took to his Twitter handle and posted a screen shot of an article confirming this replacement.
The article claimed that the cricketer-turned-politician verbally agreed to do the show, but when asked to sign the contract, he backed off.
Kapil's popular show has now been taken over by Krushna Abhishek.
The show's name has also been changed from Comedy Nights with Kapil to Comedy Nights Live.