The hard left MP claimed British constitutional conventions dictate a ruling party that can not command a House of Commons majority should step aside and let the opposition form a government.
Prime Minister Theresa May has faced widespread opposition from MPs since announcing her draft Brexit withdrawal agreement last week and faces a near impossible task to get the deal approved by Parliament.
Hundreds of lawmakers from all parties have promised to block the deal when it is put to a vote in Parliament, a date for which has not yet been set.
Mrs May is facing revolt from the Democratic Unionist Party whose power-sharing agreement props up her government and Labour have told their MPs to vote against the deal as it fails their six tests for a successful Brexit.
Meanwhile neither the SNP nor the Liberal Democrats are supporting the Brexit divorce agreement.
Most significantly, Theresa May is being criticised by Brexiteers in her own party but a plot to oust her appears stalled with the number of no-confidence letters required to trigger a leadership contest still shy of the crucial 48 figure.
Mr McDonnell tweeted that the UK is now “clearly moving into this territory” where the Prime Minister should step aside.
However the tweet was unclear as to whether Mr McDonnell was calling for a general election or expected Theresa May to hand over the keys to Number 10 to Labour leader Jeremy Corbyn.
Mr McDonnell tweeted: “Constitutional custom and practice in this country dictate that if a party in government cannot command a majority in parliament, it should stand aside and allow the opposition party the opportunity to seek to form a government.
“We are now clearly moving into this territory.”
However Mrs May still has support from her Cabinet with one member saying this morning that toppling Theresa May and her government would be “dangerous.”
Justice Secretary David Gauke said any MP’s bid to oust Theresa May was “hugely irresponsible” and urged the country to get behind the Prime Minister.
While not referring to a particular MP, he He told BBC Breakfast: “The idea that at this point, in the middle of a very delicate negotiation – that is hugely important to the future of this country – that we should remove the Prime Minister, essentially leave us leaderless for, certainly several weeks, possibly months, would be hugely irresponsible.”
The MP hit back at Brexiteers who have written to the chair of the 1922 Committee demanding a new leader that they should not talk about removing her.
He added: “What the country, I think, would expect from the Conservative Party is that we get behind our Prime Minister and make sure that she can deliver a good deal for the country.
“That’s what we are on course to do and I don’t think people should be talking about removing her at this point.
“I think that would be self-indulgent and dangerous for the country.”