Rees-Mogg, MP for North East Somerset, insisted that Ms May must prepare Britain for a possible financial crisis if the UK leaves the EU without agreement or runs the risk of losing public confidence in its government.
Writing for the Daily Telegraph, he warned how the UK after Brexit could fall into a downward spiral, recalling how Black Wednesday left the UK financial markets in total turmoil.
In 1992, the then Prime Minister, Sir John Major, was forced to withdraw the pound of the European Exchange Rate Mechanism, after the currency did not remain within the agreed limit.
This cost the UK economy an estimated loss of £ 3.3 billion pounds, sending support for Mr. Major's Government and the Conservative Party to a record low.
Opinion polls turned against the conservative party, which led in 1997 to the biggest defeat since 1906.
Rees-Mogg said: "Theresa May, the prime minister, risks putting the Conservative Party in the same position again.
"There is a possibility that we may leave the European Union without a withdrawal agreement.
"This is a perfectly manageable proposal, in fact, with the right economic policy it would be successful."
Explaining how Black Wednesday destroyed support for the Conservative Party, he added: "None of this served the Conservatives in any way.
"Since October 1992, opinion polls turned against the party, which led in 1997 to the biggest defeat since 1906.
"The economic resurgence was not credited to the Government because it occurred despite, and not because of, the Government's policies.
"John Major had dug his colors into the wrong mast in search of the European ideal and the electorate had no intention of forgiving or forgetting."
This week, Ms. May failed to make significant progress in the Brexit negotiations during her meeting with EU leaders in Brussels.
However, he remains "optimistic" in reaching an agreement with the EU before Britain leaves the bloc on March 29, 2019.
Downing Street said in a statement: "She acknowledged that there were some important issues that were still pending, but she said that the true meaning of the leaders around the table in the council was that they wanted to reach an agreement as soon as possible. Possible this fall.
"He stressed that both parties wanted to have our future relationship on track by the end of December 2020 so that endorsement would never be needed, but the negotiating teams would work hard on this to find a way forward."