Mr Crabb, MP for Preseli Pembrokeshire, who was promoted to the portfolio in March, resigned “in the best interests of my family”, he said.
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He had built his campaign on his Christian views and portrayed himself to be a family man with strong principles and morals.
He asked the woman, in her twenties, what she was going to do about his “downstairs situation” during the late-night exchange on the messaging service WhatsApp.
He had previously served as minister of state for policing and criminal justice, until being replaced in 2012.
Mr Crabb declined to comment on the story.
Crabb, who replaced Iain Duncan Smith earlier in 2016 said in a formal statement that the move is ” in the best interests of my family”.
Following the UK’s vote to leave the European Union Crabb declared his candidacy for the leadership of the Conservative party and the position of prime minister, but withdew from the race after he finished fourth in the first round of voting.
“I am grateful to my whole team for their hard work and encouragement”.
In chats on the internet messaging service WhatsApp during the run-up to the European Union referendum, Mr Crabb, the Secretary of State for Work and Pensions, insisted: ‘The public can’t expect MPs to be angels.’ He then sent a series of suggestive messages to the woman, who is in her twenties.
Crabb says he looks forward to “supporting the government’s One Nation vision from the backbenches”.
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But Jeremy Hunt remained in post as health secretary despite rumours he was for the chop.
