Jo Johnson, the universities minister, said he had been "torn between family loyalty and the national interest" and ended his message: #overandout.
He had been attending meetings of his brother's Cabinet, and said there was an "unresolvable tension".
It comes amid an unprecedented political crisis, with the prorogation of parliament looming, legislation to block a no-deal Brexit being rushed through parliament, the Prime Minister seeking to force an early election, and government whips having just stripped 21 MPs of the Conservative whip in a hugely divisive move.
Downing Street and cabinet colleagues are not thought to have had any notice of the decision. Jo Johnson indicated he would also stand down as MP for Orpington.
Mr Johnson said: “It's been an honour to represent Orpington for 9 years & to serve as a minister under three PMs.
"In recent weeks I've been torn between family loyalty and the national interest - it's an unresolvable tension & time for others to take on my roles as MP & Minister. #overandout"
Jo Johnson is pro-European and has previously called for a second referendum, a position that puts him at odds with the Prime Minister, who has vowed to leave the EU on October 31 with or without a Brexit deal.