Her comments came after Reeves unveiled plans to raise £26bn via tax rises in a Budget that also saw her scrap the two-child benefit cap.
The chancellor also extended a freeze on tax thresholds for an extra three years in a move that will drag millions into paying more tax.
Badenoch called the package "a Budget for Benefits Street, paid for by working people".
She accused Reeves of breaking promises not to raise taxes and said the chancellor should resign.
"God help us! She is spineless, shameless and completely aimless," Badenoch told MPs.
"Her speech today was an exercise in self-delusion. Today she had an opportunity to apologise and show some humility," she said.
"All we have had is wallowing in self-pity and whining about misogyny and mansplaining.
"So let me explain to the chancellor, woman to woman, that people out there are not complaining because she is female; they are complaining because she is utterly incompetent.
"Real equality means being held to the same standard as everyone else."