According to the Sunday Mirror, Mr Newmark – the Minister for Civil Society and a founder of the Women2Win campaign group – allegedly exchanged X-rated pictures over the internet with a reporter posing as a Tory PR girl.
The 56-year-old married father of five tendered his resignation after learning that the newspaper was about to publish details of their exchanges.
“I have decided to resign as Minister for Civil Society having been notified of a story to be published in a Sunday newspaper. I would like to appeal for the privacy of my family to be respected at this time,” he said in a statement.
“I remain a loyal supporter of this Government as its long term economic plan continues to deliver for the British people.”
A Downing Street spokesman said: “The Prime Minister has accepted Brooks Newmark’s resignation from his role as Minister for Civil Society.”
American-born Mr Newmark first entered Parliament as MP for Braintree in 2005.
He made his mark as a backbencher with his interventions on the economy – serving as a member of the Treasury Committee – and more recently on Syria.
He was made a Cabinet Office minister in Mr Cameron’s last reshuffle in July, having previously served a spell in the Tory whips office.
The resignation came just hours after the defection of Mark Reckless to Ukip.