Jones criticised Ms Ardern after she said "Australia has to answer to the Pacific" on climate change during a forum in Tuvalu, and suggested Prime Minister Scott Morrison "shove a sock down her throat".
Marsh, who finished the mural on Saturday after about 10 hours work, said he thought the comments were "pretty distasteful".
"It's a bit of social commentary, for starters, and then also I'm not a huge fan of Alan Jones," Marsh said.
"I thought they were pretty distasteful, and he's said a lot of things to that kind of effect in the past."
Jones has since apologised for his comments but last Saturday was threatened with the sack by employer Macquarie Radio. A number of advertisers have also abandoned his breakfast show on Sydney's 2GB and 4BC in Brisbane.
Dozens of people contacted Marsh requesting that he do a mural of the shock jock following the comments.
"I had so many, dozens of people say, 'you have to paint Alan Jones', so that was a big part of it because I didn't really have time to paint it to be honest," Marsh said.
"Alan's got a pretty big ego I think, so we'll see if he loves it or he hates it, I'm not quite sure yet," he said.
A number of people spotted Marsh painting the mural and were "super supportive of it," he said.
"They all had a few choice words about Alan Jones."
Marsh has previously painted murals in other inner Sydney locations, including depictions of former prime minister Tony Abbott marrying himself, and Mr Abbott dressed as a bride with one hand down the pants of a shirtless Cardinal George Pell.
He has also painted murals of US rapper Kanye West kissing himself, former NSW premier Mike Baird holding a glass of red wine, a kebab and a cigarette with a stack of casino chips in front of him, and late singer George Michael depicted as a saint.
A number of the artworks have been the subject of controversy and targeted by vandals.
Macquarie Media has been contacted for comment.
