Sir Alan Duncan has quit as a foreign office minister in protest against a possible Boris Johnson victory in the Conservative leadership race.
Chancellor Philip Hammond and Justice Secretary David Gauke have already said they intend to resign if he wins.
BBC assistant political editor Norman Smith said they could not stomach the prospect of a no-deal Brexit which they think Mr Johnson could oversee.
Voting for the leader closes later with the winner to be revealed on Tuesday.
The successor to Theresa May – either Mr Johnson or his rival Jeremy Hunt – will enter Downing Street on Wednesday.
Sir Alan has long been a vocal critical of the ex-foreign secretary, once describing himself as Mr Johnson’s “pooper scooper” at the Foreign Office, clearing up mess he had created.
Most recently, Sir Alan attacked his former boss over the resignation of Sir Kim Darroch, the British ambassador to the US, who stepped down after comments criticising President Trump’s administration were leaked.
Sir Alan said Mr Johnson – by failing to give his support to the ambassador – had “basically thrown our top diplomat under the bus”.
He has also previously said Mr Johnson was “the last person on Earth who would make any progress in negotiating with the EU at the moment.”
And in 2018, he described an article – in which Mr Johnson said Theresa May had “wrapped a suicide vest” around the British constitution – as “one of the most disgusting moments in modern British politics”.
The BBC’s Norman Smith said that in the resignation of Sir Alan – and the promises to quit by Mr Hammond and Mr Gauke – we were beginning to see the basis of a Tory opposition to Mr Johnson on the backbenches.
He said they – and potentially others to come – felt they could not support a prime minister comfortable with no deal and so it was better to walk now than be pushed later.
In an interview with Conservative Home, Mr Johnson said every member of his cabinet would have to be “reconciled” with the policy of leaving on 31 October – with or without a deal.
Mr Hunt has said he too is prepared to leave with no deal, but would accept a further delay, if required, to get a new withdrawal deal.
Sir Alan’s resignation was criticised by Tory MP and ex-minister Greg Hands, who tweeted: “In my view, pre-emptive ministerial resignations (If reports are true) in case your own democratically-elected party leader is not to your liking are absurd.
“And I say that as a committed Jeremy Hunt supporter. Such moves make a Corbyn government one step more likely.”
Who is Sir Alan Duncan?
He became MP for Rutland and Melton in 1992 and served as a shadow minister between 1998 and 2010.
When the coalition government came to power, he was appointed international development minister – a position he served in until 2014.
In 2016, Theresa May made him a Foreign Office minister – where he served under Boris Johnson.