Mr Newmark, 56, said: "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."
Mr Newmark, who became minister for civil society in July, entered Parliament in 2005 and was re-elected in 2010 with a majority in his Essex constituency of over 16,000.
His resignation came on the eve of the Conservative Party conference which started on Sunday in Birmingham.