Dominic Raab has warned 21 Tory rebels that "history would never forgive you", if they helped Labour leader Jeremy Corbyn become a caretaker prime minister.
His comments during a speech at the Conservative Party Conference came amid growing speculation about a potential vote of no confidence in the government.
The Foreign Secretary said: "To any of our colleagues - or former colleagues - who may just be tempted to put Jeremy Corbyn and that Momentum mob into No 10 as part of some temporary anti-Brexit coalition, I just say this: history would never forgive you."
As ITV News Political Editor Robert Peston report, Ms Beckett - former deputy leader of the Labour Party - is favourable to Mr Corbyn as she does not pose a threat to his leadership.
In any case, the Labour leader has said he will not table a motion of no confidence until he is certain Prime Minister Boris Johnson will not take the UK out the EU without a deal on October 31.
After criticising Mr Corbyn, Mr Raab said: "I say this as a passionate Brexiteer, there are some things even bigger than Brexit - and keeping that lot out of Downing Street is one of them."
He reiterated the government's main policy of taking the UK out of the EU by the Brexit deadline, saying "if the EU spurns the opportunity for a win-win deal, we will leave at the end of October - no ifs, no buts".
The government's lead on no-deal planning, Michael Gove, took the stage after Mr Raab and sought to allay concerns about what might happen in the event of no deal.
He said there will be "some turbulence" in the event of a no-deal Brexit because the Government cannot "anticipate every risk", but said preparations have "accelerated".
He told the Conservative Party Conference: "The level of our preparations has accelerated massively since Boris became Prime Minister.
"Now, of course, we can't anticipate every risk, we can't guarantee against some turbulence and that's why we'd much prefer it to secure a deal with the EU before October 31."
Commons Leader Jacob Rees-Mogg also put the boot in Mr Corbyn when he gave his speech to Conservative members.
"I do not think Jeremy Corbyn is a bad man," he said.
"But he is a weak man, too weak to lead his party."
He went on: "Behind him there may be stronger men, like Sir Keir Starmer, poised as if Brutus, stiletto in hand, awaiting the moment to strike - striking of course being something the left are quite fond of."