The ITV host announced the move on Saturday evening following new claims Mr Cummings made a second trip to Durham during the coronavirus lockdown.
The latest revelations, which put further pressure on Downing Street, comes after an investigation by the Daily Mirror and the Guardian revealed on Friday that the top aide to the Prime Minister had allegedly breached travel restrictions by travelling more than 250 miles from his home in London with his family.
Downing Street has defended the 48-year-old strategist, insisting his actions “were in line with coronavirus guidelines” and denying reports he was spoken to by the police.
The latest statement from Downing Street on Saturday evening said: “We will not waste our time answering a stream of false allegations about Mr Cummings from campaigning newspapers.”
After the new reports emerged, Mr Morgan posted on Twitter: “In light of today’s developments, I am regretfully forced to ban all cabinet ministers from appearing on @GMB until further notice.
“Only exceptions will be those who didn’t publicly support Cummings breaching a lockdown that the Govt forced on the rest of us ‘to save lives’.”
In a tweet liked thousands of times, he said: “If Boris doesn’t fire Cummings today, then I will deem the Lockdown over & drive down to see my parents (from a 2m distance) for the first time in 12 weeks.
“I’m not having one rule for these clowns & another for the rest of us.”
He also called on Mr Johnson to front the Downing Street briefing “or be damned by your cowardice”, but Transport Secretary Grant Shapps led the daily conference.
Political leaders have piled pressure on Mr Johnson to sack Mr Cummings, with the Lib Dems branding it “outrageous” and Labour saying the “country deserves answers”.