The comedian, 33, shared in a post on Instagram that the authorities have closed the case after he explained the context of the quip, which he said “hopefully amused” them.
Lycett said that the joke will remain “firmly and proudly” in his stand-up routine for the remainder of his UK and Ireland tour dates.
The stand-up shared an image of the police’s message confirming the matter was closed, captioning the post: “So someone came to my tour show a few weeks back and was offended by one of the jokes.
“And their perfectly understandable response to this was… to call the f****** police.
“To be fair to them the fuzz were very nice about it all but felt they had a duty to investigate.
“This involved me writing a statement explaining the context of the joke for them; I particularly enjoyed putting the words ‘giant donkey dick’ into a message to a police detective.
“Charmed, and hopefully amused, the rozzers have since closed the matter.”
He added: “You’ll be pleased to know that the joke – which I consider to be one of the best I’ve ever written – remains firmly and proudly in the show.
“The tour continues until September, unless I am jailed.”
Birmingham-born Lycett has appeared on a host of comedy shows over the years including Live At The Apollo, Taskmaster, Never Mind the Buzzcocks, 8 Out of 10 Cats and QI.
He became known for his stand-up routines where he would recall his humorous email exchanges when handling issues such as parking fines and scammers.
The comedian went on to front Channel 4’s consumer rights show, Joe Lycett’s Got Your Back, where he takes on large corporations on behalf of the consumer.
Lycett has also performed a number of public stunts in recent years, legally changing his name to Hugo Boss, and storming storming off the set of Steph’s Packed Lunch after the host pointed out a photo of him using a plastic bottle after he claimed he had given up using them.
He later revealed the walkout was a stunt aimed at raising awareness of single-use plastics.