Mr McDonnell, speaking to BBC Radio 4’s Today programme, said: “We believe any incoming prime minister in these circumstance should go to the country anyway and seek a mandate.”
The vote of no confidence is formally brought about through a motion in Parliament, which is debated and then voted on. If a majority of MPs vote in favour of the motion, then the government will be dissolved.
Labour will try to force a vote of no confidence in the next prime minister as soon as they take office, John McDonnell said, as Conservative candidates throw their hats into the ring to succeed Theresa May.
Asked on BBC Radio 4’s Today programme if Labour would call a no-confidence motion in the next Tory leader, the shadow chancellor said: “Yes, because we believe any incoming prime minister in these circumstance should go to the country anyway and seek a mandate.”
Mr McDonnell also said that Labour needed to have a new “conversation” about the way forward on Brexit.
Labour leader Jeremy Corbyn has been moving towards a more pro-second referendum position in recent months, saying it is on the table to stop a “damaging Conservative Brexit” if a general election cannot be achieved.
But activists want the party to endorse a second referendum in all circumstances and for Labour to back remain in such a contest.
With the backing of MPs and major trade unions, one grassroots group said it was confident of winning enough support from constituency Labour parties to have a good chance of shifting the policy at the party’s conference in the autumn.
The Tory leadership hopeful Matt Hancock said on Saturday he would refuse calls for a general election if he succeeded May, saying that to do so would be “a disaster for the country” and would risk “Corbyn by Christmas”.
When May called a general election in 2017 in an attempt to shore up her mandate she lost the Conservative party’s majority in the Commons.
McDonnell insisted that a new Tory leader would face moral pressure to call a general election in order to secure a democratic mandate. “That’s the first thing,” he told ITV News on Friday evening.
“The second thing of course [is that] we always have the opportunity of a no-confidence motion in parliament, and we will explore that. And the way in which the Conservative party remains divided, whoever is elected as their leader, there will be a prospect that some Conservative MPs now will think maybe we should go back to the country.”
The Love Socialism Hate Brexit campaigners motion states: “The leave vote is more than three years old, and there is no clear democratic mandate for any Brexit settlement. The democratic imperative now is for the people to have the final say. Labour will back remain in that public vote.”
The move comes as Remain backing parties, the Lib Dems and Change UK, revealed they could form a pact to take home more seats at the next general election.
Former Labour MP and Change UK spokesman Chuka Umunna told the Today programme: “The remain forces in this country need to work even more closely together than we have managed to achieve up to this point between now and the general election.”
He added: “I personally don’t think we should be competing at a general election and, of course, whilst we had a system of proportional representation at the European elections, it’s going to be first past the post in a general election, so we have got to get our ducks in a row and work out what configuration is appropriate for 2019 and beyond instead of just perhaps using the same model from the 1980s.”