The former Top Gear host had been due to appear on April 24 in his first BBC appearance since being dropped from the motoring show, following an attack on a producer.
Jeremy Clarkson, 54, has hosted Have I Got News For You on numerous occasions.
Jimmy Mulville, managing director of show producers Hat Trick Productions, said he expected Jeremy Clarkson to be available for a show later in the year.
He said: “On reflection, Jeremy Clarkson has decided not to host Have I Got News For You. We fully expect him to resume his hosting duties later in the year.”
Jeremy Clarkson was suspended by the BBC on March 10 following what was described at the time as a “fracas” with Top Gear producer Oisin Tymon in a hotel in North Yorkshire.
Following an internal investigation, on March 25 the broadcaster announced Jeremy Clarkson’s contract on Top Gear would not be renewed.
The BBC has announced Top Gear will continue without Jeremy Clarkson, however it is unclear whether co-presenters James May and Richard Hammond will remain.
The new series of Have I Got News For You begins on April 10 with Daniel Radcliffe as the guest host.
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