The 30-year-old forward was asked why she was wearing a jacket in training in a clip released by Chelsea and said: “Because I get called fat all the time so I have to cover it up.”
The clip was part of a mini-documentary released on Chelsea's channels called "Nothing Stops Us" where she said she was one of many women's football who feared carbohydrates.
She opened up about the "stigma" of looking fat in the game during the short film, adding: "As the game has grown, it is notable people are getting comments about their weight and how they look on TV or in photos.
"It shouldn’t matter what body type you are or how you look when you are dressed in a kit.
"It should be championed to be strong so eating more should be about doing the right thing, not just how you look on camera."
Hayes, Kirby's long-term manager at Chelsea, praised the England star for speaking openly and hopes it helps other players, who risk developing eating disorders in the football environment.
"I am proud of Fran for saying that," Hayes said. "As women, we are judged enough to look a certain way but to perform at the level that you need to, then you need to eat carbs as well as a healthy diet.
"There is a problem in the game, not just the women’s game, but in sport with under-fuelling and loading and that comes with constant demands to look a certain way, and, unfortunately, there's a vitriolic environment on social media.
"Unfortunately, Fran has been a victim of that, as have other players. Again, I urge everyone to be mindful of that because we’re destroying people in many ways.
"I am glad Fran said what many female players feel. All female footballers discuss this in the background."
Hayes would like to see weigh-ins or body composition tests taken out of women's football and urges broadcasters, photographers and media to be mindful of body shaming.
Kirby, meanwhile, is widely regarded as a Chelsea legend and one of English football's most exciting talents in recent years. But she has had a torrid time of health and injury issues since developing pericarditis in 2020, a painful inflammation of the fibrous sac.
The 67-cap attacker also missed the World Cup this summer through a serious knee injury but Hayes thinks her forward is closing in on her best form once again.
"She is starting to look and feel like herself again," she added. "She’s starting to see things, pictures in her game which are normally quite natural to her, they are coming back.
"She seems in a good place and I had a chat with her about it yesterday. Long may it continue because she is a national treasure.
"It is my job to make sure she stays on the pitch, as it is Sarina's [Wiegman] because both England and Chelsea are better for it."
Chelsea face Aston Villa in the Women's Super League on Saturday but are without Melanie Leupolz, Guro Reiten and Katerina Svitkova.