Speaking to the BBC, Badenoch criticised Reeves for “making a hoo-ha about being the first woman to present a Budget”.
“Bringing in your identity cheapens achievement,” Badenoch said.
If the Budget is “bad, that’s not great for women,” she added.
She told Nick Robinson she considered “pulling my punches” because Reeves looked “absolutely broken” after an embarrassing leak by the Office for Budget Responsibility (OBR) exposed most of the Budget 40 minutes before she spoke.
“Then [Reeves] launched into the most extraordinary tirade against Conservatives in her own speech – so she started it,” Badenoch said.
Her comments came under criticism from some, including ex-Lib Dem leader Tim Farron who said there was “absolutely no need” for the “barrage of personal abuse”.
But Badenoch dismissed claims she had descended to “playground abuse” with her comments.
“You can’t please everybody,” she said.
“I’ve taken on a tough job and I’ve got to do it the way anybody else has to.
“I don’t complain about it, I don’t say it’s misogyny or racism or anything like that,” Badenoch said.
Badenoch also claimed she had to suffer “a barrage of abuse every single week at Prime Minister’s Questions” where Sir Keir Starmer “can get very personal”.