Clarkson caused controversy during an appearance on The One Show last month when he said that people on strike should be shot in front of their families.
The Top Gear host, who has apologised and said he was joking, was also slammed for suggesting that trains should not stop for people who have committed suicide by jumping onto the tracks.
David Cameron and Dame Joan Bakewell were among the personalities who later criticised Clarkson for his remarks.
BBC executives have now decided not to air an episode of QI featuring Clarkson this evening, The Guardian reports.
Insiders allegedly claimed that the decision was taken because it is believed that it is too soon for Clarkson to appear on screen.
"It's not to do with anything specific that Clarkson said on QI," a source explained. "It is more a case of the BBC not wanting to look as though it didn't care about the storm and putting Clarkson back on screen as if nothing had happened."
The episode also featured Ross Noble and Dara O'Briain alongside regular panellist Alan Davies and was recorded in the summer.
BBC Two is now expected to air a different instalment of the comedy show, starring Sandi Toksvig, Lee Mack and Jimmy Carr.
A spokesperson for the BBC said: "It is not unusual for the running order of programmes to change. The billed episode of QI will be shown at a later date."
> Jeremy Clarkson's One Show rant complaints top 31,000