A Conservative spokesman has told this newspaper there is “no need” to cite the project despite it not yet being voted through because it was announced last year.
The concession comes after Tory MPs threatened to publicly disavow the election manifesto if it explicitly promised Heathrow expansion.
There were also fears it would have lost voters in crucial London marginal seats which the Liberal Democrats want to take from the Tories.
Both Mr Johnson, the Foreign Secretary, and Justine Greening, the Education Secretary, are ardent opponents of a Heathrow third runway.
Mrs May backed Heathrow expansion last year, completing an about-turn from the Tories who had campaigned against the third runway in the 2010 election.
The decision was expected to be included in this year’s manifesto because it will be one of the most expensive and controversial infrastructure projects if she wins re-eleciton.
However a Tory spokesman said: “There is no need for Heathrow to be in the manifesto because the decision was taken by the Government last year.”
A more veiled reference to airport expansion is now expected to be included instead.
There is no suggestion that the Tories are abandoning their policy of building the third runway, which is currently out to consultation.
However leaving it out of the manifesto solves a political problem brewing behind the scenes because up to a dozen Tory MPs are staunch opponents of the move.
Mr Johnson, who once promised to lie down "in front of those bulldozers and stop the building", joined the legal case against the expansion while London Mayor.
The Foreign Secretary would have had to publicly disown any Tory manifesto promise that the third runway would go ahead during the campaign.
Zac Goldsmith, who triggered a by-election after Heathrow was approved only to lose, faced a similar problem as he battles for re-election in Richmond Park next month.
He told The Telegraph he would “of course” oppose the third runway while campaigning over the coming weeks.
“Heathrow expansion matters to many people in our community, and it is so clearly the wrong answer. I'm determined to win the argument in Parliament and I think I can,” he said.
Tania Mathias, the Tory MP for Twickenham facing a tough battle to defeat Sir Vince Cable of the Liberal Democrats, said similar.
“I have not missed a heartbeat in the campaign, even though an election has been called,” she told The Telegraph.
“As far as I’m concern, the public consultations are still ongoing. I am doing public meetings as I would continue to do. There is absolutely no change in the momentum against Heathrow expansion.”
A third Tory MP said: “I don’t agree with Heathrow expansion. If there is a vote in Parliament I would vote against. My position has been pretty consistent on this. I won’t be supporting it.”
Critics are expected to jump on the news because they argue the legal approval for Heathrow expansion can only come after a vote in Parliament.
The Tory government is also facing a legal challenge from four councils including Maidenhead and Windsor - in Mrs May’s constituency - while remains ongoing.