She claimed last season's suspension due to COVID-19 benefitted Leeds in their promotion to the top flight.
The football community condemned Leeds' tweet with Rapinoe the latest high-profile figure to throw her support behind Carney.
On Twitter, the US star wrote: "Shame. Shame. Shame. Thicken up that skin y'all. Also, don't come for @karenjcarney she's a National treasure."
Leeds have since condemned the social media abuse aimed at the former England international.
A club spokesperson said: "Leeds United completely condemns any abuse received by Karen Carney on social media following last night's Premier League game with West Bromwich Albion.
"Everyone at our club respects Karen greatly for all she has achieved in the game, as well as her work in the media and the charity work she undertakes."
Leeds owner Andrea Radrizzani defended the club's tweet, saying: "I'm very sorry Karen was abused on social media.
"I wanted to defend my club and our players from a comment which I felt was harsh from Karen on air. Our tweet wasn't offensive - simply stating that we won the league by 10 points.
"We honestly didn't expect such a reaction and we are sorry she experienced that. I respect her as a person and a pundit and I hope she understands that we just want to defend our club, we are a family.
"I hope the abuse stops and we can move forward and I hope Karen will be our guest at Elland Road soon - I'd like to meet personally with her."
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