Mr McCarthy, who has a chance of becoming Speaker of the House after 2022’s midterms if Republicans retake the 435-seat chamber, will require the support of his caucus to do so.
Ms Greene, who was elected to Congress in November 2020 on a pro-Trump platform, told a podcast on Thursday that he “doesn’t have the full support” of House Republicans.
The pair have disagreed on a number of issues since January 2021, including whether or not anti-Trump Republicans should be removed from committee assignments.
Ms Greene told fellow agitator and member of Congress Matt Gaetz’s Firebrand podcast that she felt Mr McCarthy had forgotten her and other pro-Trump Republicans.
“We know that Kevin McCarthy has a problem in our conference. He doesn’t have the full support to be speaker,” she told Mr Gaetz. “He doesn’t have the votes that are there.”
She carried on: “Because there’s many of us that are very unhappy about the failure to hold Republicans accountable, while conservatives like me, Paul Gosar, and many others just constantly take the abuse by the Democrats.”
The reference to Mr Gosar, who was censured and ousted from his committee assignments last week, comes after McCarthy appeared to suggest he would restore assignments taken from Ms Greene in February following an outcry at her social media history.
Mr Gosar was meanwhile condemned by Democrats for sharing an animation in which he killed US President Joe Biden and congresswoman Alexandria Ocasio-Cortez.
Republicans including Ms Greene largely attacked the move to censure Mr Gosar, while Democrats accused Mr McCarthy of failing to penalise members of his own caucus for wrongdoing.