Jimmy Mulville, managing director of Hat Trick Productions which makes Have I Got News For You, said: "On reflection, Jeremy Clarkson has decided not to host the show. We fully expect him to resume his hosting duties later in the year."
He had been due to record his appearance on Have I Got News For You on April 23 to be broadcast on April 24.
The star was suspended by the BBC on March 10 after he attacked Top Gear producer Oisin Tymon, splitting his lip and verbally abusing him.
Clarkson's contract was not renewed, with director-general Tony Hall saying at the time "a line has been crossed" and "there cannot be one rule for one and one rule for another".
But the star received widespread public support in the aftermath of the fracas, and one million people signed a petition calling for the BBC to reinstate him.
hnews@herald.ie