Barton has been heavily criticised after suggesting that women “shouldn’t be talking with any kind of authority” on men’s football.
The one-cap England international, sacked by Bristol Rovers in October, has since doubled down on his comments on X (formerly Twitter), saying that “you cannot watch a game now without hearing the nonsense”.
Presenter Woods fronts TNT Sports’ coverage of the Premier League and Champions League, and has also worked for ITV, talkSPORT and Amazon.
She has accused Barton of creating a “pile on” with his remarks.
“Joey’s entitled to his opinion,” Woods said on X. “If he feels that strongly about women in the men’s game he could ask for a private conversation with the broadcasters & state his case.
“These tweets only encourage a pile on for the women getting on with their jobs. Or was that the intention?”
Barton’s stream of posts on the matter have continued into a second day after initially posting on social media during Prime Video’s coverage of Wednesday night’s Premier League action.
“Women shouldn’t be talking with any kind of authority in the men’s game,” Barton wrote initially. “Come on. Let’s be serious. It’s a completely different game.
“If you don’t accept that. We will always see things differently. The women’s game is thriving. Fantastic to see. I cannot take a thing they say serious in the men’s arena.”
As part of his comments, Barton shared a clip of a post on Manchester City’s Instagram account that featured a female broadcaster making a small error.
Barton has also suggested that any men that have criticised him and support female broadcasters are “eunuchs”.
Responding directly to the clip, Woods suggested that while she and Barton had previously “got on”, his singling out of the young presenter was “wrong”.
She said: “Usually avoid these conversations as I don’t like adding more oxygen. But throwing young vloggers to the wolves is wrong.
“I started my career vlogging & I’ve always got on with Joey. He also sent me a lovely good luck message for TNT in June. Does that make him a eunuch too?”