Labour MP John Mann is leaving the House of Commons after 18 years to become a member of the House of Lords.
In July, he was appointed by outgoing PM Theresa May to head a government inquiry on tackling anti-Semitism.
Mr Mann chaired a cross-party parliamentary group on anti-Semitism and has been a frequent critic of Mr Corbyn's handling of the issue.
His departure could trigger a by-election in his Nottinghamshire constituency of Bassetlaw.
The BBC's Parliamentary Correspondent Mark D'Arcy said "Mr Mann's Bassetlaw seat is precisely the kind of pro-Brexit blue collar seat the Conservatives will be targeting at the next election, so a by-election there (if not overtaken by an early general election) would be quite an event."
Mr Mann was nominated to the House of Lords in Theresa May's resignation honour's list, despite having previously called for the House of Lord to be abolished.
Speaking to the Yorkshire Post, he said Parliament had been "paralysed" by the political situation.
"The power of the Prime Minister, Speaker and the whips will all need to be reconsidered if our democracy is to properly function - I am not holding my breath at such maturity," he said.
He was one of the 19 Labour MPs who voted for Boris Johnson's Brexit bill at second reading in Parliament.
Mr Mann became MP for Bassetlaw in 2001 and served on the Treasury Committee from 2003.