Mr Young had been discussing abusive messages on Twitter whilst on the BBC programme along with Labour MP Stella Creasy, who had been subject to abuse herself.
The tweet, which was deleted minutes after being posted, mocked Mr Young, author of How to Lose Friends and Alienate People, who tweets under the handle @toadmeister.
The force posted an update on Wednesday morning apologising for the tweet, saying: “We apologise for the tweet sent to @toadmeister & for any upset caused. The matter is being investigated & we’re reviewing Twitter access.”
Mr Young replied to the message, saying that he ‘wasn’t offended’ and would not be making any complaint.