The BBC announced this week that the comedy panel programme was ending after 17 years, with Ó Briain quipping: "That's it folks, the UK has finally run out of news."
Neil, 73, then tweeted “Mock the Week deserved to be cancelled” and linked to a news article that had the same title.
Comedian Ó Briain snapped straight back with a dig of his own, seemingly referring to the fact that former GB News chairman Neil took a break from the channel two weeks after it launched and went on to quit.
He tweeted: "Still, at least I didn’t bail on it after two weeks and f*** off to my house in France, eh Andrew?"
"All the best!" added the 50-year-old.
Fans were thoroughly amused by his comment.
"This can't be shared enough," one person posted on Twitter.
"This has cheered me up no end!!!" said someone else, adding a string of crying with laughter emojis.
Another person called it a "genius reply".
— Andrew Neil (@afneil) August 3, 2022
Mock The Week started in 2005 and Ó Briain has been on the show throughout its long run.
Its end was announced this week, with a BBC spokesperson saying in a statement: “The next series of Mock The Week will be the last, we are really proud of the show but after 21 series we have taken the difficult decision in order to create room for new shows.”
Ó Briain said: “That’s it folks; the UK has finally run out of news.
"The storylines were getting crazier and crazier; Global pandemics, divorce from Europe, novelty short-term prime ministers.
"It couldn’t go on."
Watch: Mock The Week's best moments as show ends