The hardline Brexiteer made the quip on Twitter after Galen Milne was sacked as a candidate for Jo Swinson's party over the horrific Facebook comment.
Mr Milne called for Mr Rees-Mogg, Boris Johnson, Liam Fox, Michael Gove and David Davis to be 'hung, drawn and quartered, with each quarter being sent to the 4 corners of the UK to be burned at the stake'.
The brutal and sadistic punishment was handed out in the Middle Ages in England to men found guilty of high treason.
In response to the sickening Facebook outburst, Mr Rees-Mogg dryly tweeted that his Cabinet position meant he would avoid such a fate.
'Typical Lib Dem. Mr Milne should get his facts straight,' he wrote.
'As Lord President of the Council, I am entitled to the privilege of being beheaded.'
Scottish Lib Dem candidate Galen Milne is sad to have made the outburst against senior Tory Brexiteers on Facebook
In response to the sickening Facebook outburst, Mr Rees-Mogg dryly tweeted that his Cabinet position meant he would avoid such a fate
Lord President of the Council is a title given by convention to a Cabinet minister which sees them chair Privy Council meetings.
Hanging, drawing and quartering was a horrific punishment handed out to people including Scottish freedom fighter William Wallace.
It involves the victim being hanged briefly so they do not die, before being drawn - having their internal organs removed and burned in front of their face - before their body was cut into four.
The pieces often sent to different parts of the country as a warning against rebelling against the monarch.
Mr Milne apologised this afternoon, saying: 'I deeply regret the offensive statements on social media. I want to apologise to anyone that I have offended.'
A Scottish Lib Dem spokesman added: 'Such language is unacceptable and offensive. Galen Milne will not be a Liberal Democrat candidate at the General Election.'
The row came as Ms Swinson complained that the Brexit on offer under Boris Johnson is 'not what people were promised' as she clashed with Piers Morgan over her party's plan to keep the UK in the EU today.
The Lib Dem leader vowed to campaign at the next general election to revoke article 50 and ignore the result of the referendum, telling the Good Morning Britain host: 'Democracy did not end on 23 June 2016.'
Ms Swinson clashed with Piers Morgan on GMB this morning, appearing live from the Lib Dem conference in Bournemouth
Party members voted yesterday at the Lib Dem conference in Brighton to campaign to stop Brexit entirely if there is election.
But the party will seek a second referendum until that happens, with MPs currently blocking the Prime Minister's attempts to go to the country.
It came as Boris Johnson heads to the continent for a crucial Brexit showdown with Jean-Claude Juncker.
Ahead of his first talks with the EU commission president, the PM insisted he is 'passionate' about getting a deal and hailed 'signs of movement'.
Ms Swinson told GMB: 'The government has gone away taken the result of that referendum and negotiated what that will mean for the British public.
'What is on offer today is not what people were promised.'