A senior source in the whips office said MPs "will have the whip withdrawn and will not stand as candidates in an election" if they fail to vote with the government when MPs return to Parliament on Tuesday.
"The whips are telling Conservative MPs today a very simple message - if they fail to vote with the government on Tuesday they will be destroying the government’s negotiating position and handing control of Parliament to ," the senior government source said.
The source continued: "Any Conservative MP who does this will have the whip withdrawn and will not stand as Conservative candidates in an election.
"There is a chance of a deal on October 17 only because Brussels realises the prime minister is totally committed to leaving on October 31.
"All MPs face a simple choice on Tuesday: to vote with the government and preserve the chance of a deal or vote with Corbyn and destroy any chance of a deal."
Explaining the deselection policy on behalf of the government was former chief whip Gavin Williamson, who told ITV News: "It is about making sure that the prime minister is in the best possible position to go to Europe and get the best deal from Europe.
"Everyone of those members of the conservative party needs to be rallying behind the prime minister, it's what's expected."
He added: "It's a three-line whip, it's perfectly acceptable on something as important as this, to make sure that all Conservative members of Parliament are backing the prime minister."
A senior Number 10 source told ITV News: "If we don't deliver Brexit, there will be no Tory Party - stopping it happen is insane."
A group of anti-no deal Tory rebels, which includes the former Chancellor Philip Hammond, told ITV News it was "sheer hypocrisy".
"Almost a quarter of the current cabinet have voted against the party whip," they said.
"But this is about national interest, and we've moved beyond the point where threats will persuade people to abandon their principles," they added.
The PM instead only invited Mr Hammond for a one-to-one meeting, but ITV News has been told the former chancellor has declined the invitation.
The purpose of the meeting had been to attempt to dissuade them from voting for legislation compelling him to seek a Brexit delay.
But a source close to the group said: "Aside from being deeply discourteous, today's behaviour shows this is not a government interested in compromise.
"These MPs want proof that there is a genuine and sincere attempt to get a deal. The fact that the prime minister isn't even prepared to meet them suggests there isn't."
He told Sky News before this announcement: "Sometimes there is a point where... you have to judge between your own personal interests and the national interest. And the national interest has to come first."
"But, I hope it doesn't come to that, and I hope cooler and calmer heads will look at this and think that trying to split the Conservative Party in this way is not a sensible way forward for the Conservative Party, or indeed for the country," he added.
Asked if the move was hypocritical, a Number 10 source said this is a "different situation - this is a existential crisis for the Tory party."