Ms Badenoch claimed Mr Hughes was forced out for revealing that Ms Reeves had potentially misled the public about a spending black hole, despite the OBR informing her of a £4bn surplus.
Mr Hughes officially resigned over a leak of Budget details 40 minutes before its delivery, attributed to a long-standing systematic problem.
The accusation was made during Prime Minister's Questions, where Sir Keir Starmer defended his government's economic record and praised Mr Hughes.
Ms Reeves left PMQs before an urgent question on Mr Hughes' resignation, leaving her deputy to respond, as pressure mounts on her position.