Mr Johnson is being urged to hand over to a caretaker prime minister.
If the Government is defeated it would almost certainly trigger a general election.
That eventuality is unlikely, as a significant number of Tory MPs would need to vote against the Prime Minister – or at least abstain.
Mr Johnson had been expected to open the debate – although it is not clear whether he will now do so.
Prime Minister Boris Johnson Outside Number 10, Downing Street Dominic Lipinski
Unusually, the vote will take place on a Government motion.
Labour had originally said it would seek to hold a confidence vote as Mr Johnson plans to stay on as Prime Minister until the autumn, when a new Conservative leader will be in place.
But the Government refused to accept the wording of the Labour motion, which expressed no confidence in the Government and the Prime Minister, effectively forcing Tory MPs to go on record saying they still had confidence in Mr Johnson if they wanted to avoid an election.
Instead, ministers tabled a motion of their own after Commons Deputy Speaker Nigel Evans told the two parties to resolve the matter themselves.
Ahead of the vote, Liberal Democrat leader Sir Ed Davey, who has tabled an amendment demanding Mr Johnson resign immediately, said: “Conservative MPs have the chance to show they are listening to the people by getting rid of this failing Prime Minister.
“Boris Johnson should go now and, when a new Conservative leader is in place, we should have a general election so that people can kick out these Conservatives once and for all.”
Tory MPs will cast their votes on Monday, in the third round of the contest to find a successor to Boris Johnson.
They will vote from 5pm, with chairman of the 1922 Committee Sir Graham Brady expected to announce the results at 8pm.
Once whittled down to four, there will be another round of voting on Tuesday – and, if no one pulls out, the leadership race will be reduced to two candidates by Wednesday.
The final two will then campaign to win over the party membership, before a winner is confirmed in September.
The Prime Minister is being urged by some to leave before the Autumn James Manning
Sir Keir Starmer will be hoping for a general election Owen Humphreys