The war of words was sparked when the Leader of the Scottish Conservatives, Douglas Ross, called on the PM to resign after he admitted attending a drinks party in the Downing Street garden on 20 May, 2020 when the country was in lockdown.
Defending the prime minister, Rees-Mogg dismissed the Scottish leader as “quite a lightweight figure” in the Conservative Party.
"I don’t think Douglas Ross is a big figure," the Leader of the House of Commons said when asked how significant Ross' intervention was.
He added: "He has been constantly in opposition to the prime minister, he opposed Brexit, he is not somebody who you would ever expect to say helpful things about the prime minister."
The comments have sparked fury, particularly in Scotland.
In a dig at Rees-Mogg, who was infamously photographed laid out horizontally on the House of Commons benches, Scottish Conservative MSP Jamie Greene told him to “have a long lie down”.
The party’s justice spokesman at Holyrood said: “(Mr Rees-Mogg) should go and have a long lie down, maybe not in the House of Commons.”
Ross himself said: “Jacob Rees-Mogg, as anyone, is entitled to their opinions. I don’t have to agree with them.”
The Scottish leader had previously been an open supporter of the prime minister, and voted for him in the Conservative Party leadership contest.
Ross's sentiment was echoed by former Scottish Conservatives leader, Ruth Davidson, who said Ross's decision was "a tough call" but "the right one".
Scottish National Party MSP Karen Adam described the comments as "sickening".
"This is what they do, throw folk under the bus," she said.
"If that’s how they feel about their own in Scotland then what do they think of us? Or vulnerable folk. Treating Scotland with utter contempt.
"JRM is displaying vile narcissistic behaviour - discard and smear campaign."
Tim Montgomerie, founder of the ConservativeHome website, called on Rees-Mogg to apologise: "I urge you to apologise ASAP for the personal+playground way you dismissed Douglas Ross", he said.
"Johnson uber-loyalists risk looking like you're willing to trash colleagues and anyone who dares to think a new PM is necessary. Stop it. Now."
Four Tory MPs have called for the PM to go, but the majority of Johnson's Cabinet have publicly backed him to continue in the role for now.
Watch: Scottish Tory leader Douglas Ross calls for PM to resign over Number 10 party row