The prime minister's official spokesman said she would fight any attempt to oust her if the required 48 Tory MPs called for a contest.
"We believe it is important to maintain more flexibility in how we're dealing with services", May told parliament.
It follows concerns raised over Theresa May's Brexit plan which she forward at Chequers on Friday.
"The general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one", Davis said in his resignation letter to May.
"In a resignation letter, Davis said the "'common rule book' policy hands control of large swathes of our economy to the European Union and is certainly not returning control of our laws in any real sense".
The value of the British pound dropped on global markets after Johnson's announcement, having risen after the announcement Friday that a Cabinet deal on Brexit had been agreed.
Davis quit just days after May had claimed she secured senior ministers' approval for a deal with how the United Kingdom was going to leave the Brussels club.
"It seems to me that the national interest requires a Secretary of State in my Department that is an enthusiastic believer in your approach, and not merely a reluctant conscript".
Davis said he could not support May's plan to maintain close trade and regulatory ties with the European Union, which he said gave "too much away, too easily".
Ministers signed off on a blueprint for a new U.K. -EU "free trade area", with interwoven customs regimes, and identical regulations for industrial and agri-food goods.
David Lammy, a prominent member of the opposition Labour party, derided Davis as "a man who cant take responsibility". Brexit-supporting lawmakers were angered by the proposals, saying they would keep Britain tethered to the bloc and unable to change its rules to strike new trade deals around the world. They had been trying to work out how she and a 45-year-old man had come into contact with Novichok.
Brexit ministers are resigning from their posts and PM May is set to face a challenge from political foes in the near future over her quickly-failing soft Brexit proposal.
"What matters for GBP markets is the type of Brexit delivered - not who delivers".