He added he would "listen to what the Prime Minister has got to say on Monday evening at the 1922 Committee" before deciding what action to take.
Davis's resignation could embolden Brexit-supporting Conservative parliamentarians to challenge May's leadership.
The staunchly pro-Brexit Conservative MP Andrea Jenkyns tweeted: "Fantastic news. Well done David Davis for having the principle and guts to resign".
The resignation may also further complicate an already fraught Brexit, with less than nine months before Britain leaves and just over three before the European Union says it wants a deal that will mark Britain's biggest foreign and trade policy shift in decades. There was no immediate comment from Baker.
May will have a key meeting with members of her Tory party to discuss her plan in Parliament on Monday.
Less than nine months remain until Britain leaves the bloc on March 29, 2019.
They say Britain should have a clean break from the bloc and be liberated to pursue new trade deals with other countries, as well as to make its own laws, free from European influence.
Iran executes eight over deadly IS attacks Iran's paramilitary Revolutionary Guard responded to the attack by launching six missiles into eastern Syria, targeting ISIL. A total of 22 people - 17 civilians and 5 assailants - were killed during the attacks.
"In his 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". "Parliament will decide whether or not to back the deal the Government negotiates, but that deal will undoubtedly mean the returning of powers from Brussels to the United Kingdom".
"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", he wrote.
He said that it looked "less and less likely" the party would deliver on the Brexit result.
Arch-Brexiteer Jacob Rees-Mogg hit out at the "defeatism" in the Government's plans, warning that he would vote against them - and suggested other Eurosceptics may do the same.
Johnson has not commented publicly since Friday. Michael Gove, May's environment minister, said on Sunday that while the agreed negotiating stance was not flawless, he believed it delivered on handing back control to Britain. Environment Secretary Michael Gove said Sunday that it did not contain everything he wanted but "I'm a realist".
David Davis' resignation comes days after Theresa May secured the cabinet's backing for her Brexit plan despite claims from Brexit supporters, known as Breexiters, that it was too "soft", BBC News reports.