Jo Johnson, the younger brother of Prime Minister Boris Johnson, is resigning as an MP and minister, saying he is "torn between family loyalty and the national interest".
The business minister and Tory MP for Orpington, south-east London, cited an "unresolvable tension" in his role.
Mr Johnson voted Remain in the 2016 EU membership referendum, while his brother co-led the Leave campaign.
BBC political editor Laura Kuenssberg said it was "unbelievable timing".
Mr Johnson's resignation follows the removal of the Tory whip from 21 MPs this week for supporting moves to prevent a no-deal Brexit.
Our political editor tweeted that Mr Johnson was "understood to be upset about the purge of colleagues" and that the brothers were "in very different places" on Brexit.
Jo Johnson resigned as a minister last year in protest at Theresa May's Brexit deal.
But he re-entered government during the summer, after Conservative Party members elected his brother as leader.
Mr Johnson's resignation also comes as the government announced it would give MPs another chance to vote for an early election on Monday.
The fresh vote on an early election is scheduled just before Parliament is due to be prorogued - or suspended - from next week until 14 October.
A Downing Street spokesman said: "The prime minister would like to thank Jo Johnson for his service. He has been a brilliant, talented minister and a fantastic MP.
"The PM, as both a politician and brother, understands this will not have been an easy matter for Jo. The constituents of Orpington could not have asked for a better representative."
Former cabinet minister David Gauke, one of the MPs who lost the Conservative whip, tweeted: "Lots of MPs have had to wrestle with conflicting loyalties in recent weeks. None more so than Jo. This is a big loss to Parliament, the government and the Conservative Party."
Labour's shadow education secretary Angela Rayner said: "Boris Johnson poses such a threat that even his own brother doesn't trust him."
Brexit Party leader Nigel Farage said the resignation showed the "centre of gravity in the Conservative party is shifting rapidly".
But, in a tweet, Rachel Johnson, the Remain-supporting sister of Boris and Jo Johnson, said "the family avoids the topic of Brexit, especially at meals, as we don't want to gang up on the PM".