Conservative MP for Braintree, Brooks Newmark, has stepped down as Minister for Civil Society, over allegations to be published in a Sunday newspaper.
The details of the story, due to appear in the Sunday Mirror tomorrow, have not been disclosed, but it is believed the MP exchanged sexual images over social media.
Mr Newmark, 56, said: "I would like to appeal for the privacy of my family to be respected at this time. I remain a loyal supporter of this Government as its long-term economic plan continues to deliver for the British people."
Mr Newmark was elected MP for Braintree in 2005. The married father of five was appointed a Cabinet Office minister as part of David Cameron's last reshuffle in July.
A Downing Street spokesman issued a statement confirming the Prime Minister has accepted Mr Newmark's resignation.
No 10 said later that Rob Wilson, Conservative MP for Reading East, had been appointed as Mr Newmark's replacement as minister for civil society.
Newmark's resignation is another blow to the Conservative party, coming just hours after fellow Tory MP Mark Reckless said he was quitting the party to join UKIP.
The two announcements come on the eve of the Conservative party conference which is due to get under way in Birmingham on Sunday.