May has accepted Davis' resignation, according to a statement from her office.
Davis, who was appointed Brexit secretary in 2016, was responsible for negotiating Britain's withdrawal from the European Union.
One leading local newspaper, the Daily Telegraph, said Monday his shock decision has plunged May's minority government into a crisis.
Steve Baker, a Conservative MP and Brexit minister in Davis' department also quit the government following May's proposals.
The double blow for May came as she is preparing to address the House of Commons on the proposals agreed at her day-long meeting Friday at Chequers, her country retreat.
Peter Bone, another Conservative MP, backed Davis' decision, saying that he had done the right thing and it was a principled and brave decision.
"The prime minister's proposals for a Brexit in name only are not acceptable," said Bone.