Downing Street responded with a terse statement.
Jo Johnson's resignation, and his call for a fresh referendum to test voter sentiment, further complicates matters for May as she tries to strike a deal with European Union leaders that would pass muster with her own cabinet and win backing in Parliament.
In an article published online, Johnson backed his brother Boris, who also quit the government earlier this year in protest against May's handling of Brexit negotiations.
Stanley Johnson, the father of Jo Johnson, has said he is "very proud" of his son following his resignation from the government over Brexit.
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Mr Johnson also joined other senior Tories, such as former education secretary Justine Greening and ex-business minister Anna Soubry, to demand a second referendum.
"Jo Johnson is the eighteenth minister to resign from Theresa May's government".
"Britain stands on the brink of the greatest crisis since the Second World War". "To do anything less will do grave damage to our democracy". We will not under any circumstances have a second referendum.
Like rats, "in London, you're never more than a few feet from at least two Johnsons" joked Rachel Johnson in an article previous year.
'It is now my intention to vote against this Withdrawal Agreement.
Boris congratulated him on his decision via Twitter.
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Johnson slammed Theresa May's proposals, writing: "My brother Boris... recently observed that the proposed arrangements were "substantially worse than staying in the EU".
Labour Shadow Brexit Minister Jenny Chapman said that Theresa May had "lost all authority and is incapable of negotiating a Brexit deal within her own party, let alone with the EU".
Lib Dem leader Sir Vince Cable, whose party supports calls for a "People's Vote" on the final deal, said: "We warmly welcome Jo Johnson's support of the campaign to give the people the final say on the deal and a chance to exit from Brexit".
In a tweet, Boris said he had "boundless admiration" for his brother and that they are "united in dismay" at the indefensibility of May's position even though they disagree over Brexit.
Jo Johnson, younger brother of former Foreign Secretary Boris Johnson, said the withdrawal agreement being discussed by European Union and British leaders would greatly weaken Britain and require the country to follow European Union rules without having any say. "On that he is unquestionably right", he said.
Boris said he had "boundless admiration" for Jo and that he and his brother were "at the intellectually and politically indefensible of the United Kingdom position".
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