The leading Eurosceptic, who attended Eton College, said other MPs who went to school at Winchester College were "characteristically...highly intelligent but fundamentally wrong".
He made the comments during a debate on Brexit as MPs prepared to hold a series of crunch votes on the UK's withdrawal from the EU.
The "indicative votes" on a range of possible Brexit outcomes came after backbenchers, led by Conservative former ministers Sir Oliver Letwin and Nick Boles, seized control of the Commons agenda.
Mr Rees-Mogg criticised the move, saying it was "constitutionally ill thought-through". He claimed that Tory MPs who did not have faith in the government to manage Commons proceedings should vote against it in a confidence motion.
That prompted Mr Boles to interject to say he was "quite capable of distinguishing between my general confidence in the government...and their specific conduct on this particular issue." The former minister said he had repeatedly supported the government by voting for its Brexit deal, which Mr Rees-Mogg has twice voted against.
In response, Mr Rees-Mogg said Mr Boles' argument was "characteristically Wykehamist - highly intelligent but fundamentally wrong". The word "Wykehamist" is used to refer to someone who went to Winchester College.
Turning his guns on Sir Oliver, another alumnus of Eton College, Mr Rees-Mogg added: "I must confess I've sometimes thought my right honourable friend for West Dorset was more a Wykehamist than of my own school."
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Defending his decision to push ahead with the plan for indicative votes, the former cabinet minister had earlier told MPs that the proposal was only needed because "Whitehall has failed".
He said: "In an emergency the House of Commons is capable of controlling its own business in such a way as to find a solution the vast majesties of Whitehall and government have not been able to provide us with.
"It's because Whitehall has failed, not due to the inadequacy of any individual but due to the basic difficulty of the situation, that the Commons is taking these steps."
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