The Foreign Secretary, who pledged to lie down in front of bulldozers to block a third runway being built at the west London airport, said his resignation over the issue would “achieve nothing”.
Government frontbenchers are bound by “collective responsibility” to support official policy.
Most Tory MPs are expected to back Prime Minister Theresa May and vote for Heathrow expansion, but Mr Johnson will be abroad.
The Foreign Office said he would be on a trip out of the country, but could not give any further details for security reasons.
After a period of silence, a letter from Mr Johnson to his constituents defending his absence was obtained by the Evening Standard.
The Uxbridge MP wrote: “My resignation would have achieved absolutely nothing.”
He also predicted the third runway would never be built.
It follows fellow London MP Greg Hands quitting as trade minister to vote against the expansion.
“Tonight is about fulfilling that pledge in exactly that way,” Mr Hands told Sky News on Monday.
“I think the impact of Heathrow expansion will be considerable and detrimental in my constituency – more widely I think it’s the wrong decision.”
He was abroad when he quit as a minister, but landed back in London today to make the vote.
Tory MP Justine Greening, who left the government in January and also opposes Heathrow expansion, tweeted: “Great you’re back Greg! I wouldn’t want any long-term MP campaigners against Heathrow expansion to miss their chance to represent their community. #commitment #bulldozer.”
Earlier, Transport Secretary Chris Grayling called the vote “the biggest transport decision in a generation”.
He also admitted he “didn’t know where” Mr Johnson was.
But Mr Grayling added: “We all fought a general election on the manifesto of expanding Heathrow Airport.
“But equally, where there are people who’ve got particular constituency issues, we’ve left them the freedom to carry on expressing the views we’ve always had.”
Senior Tory backbencher Dr Sarah Wollaston has called on the foreign secretary to resign.
She said the decision to let Mr Johnson avoid a three-line whip in support of the Heathrow plan by “won’t wash”.
“I think this would be an opportunity for a colleague like Boris Johnson to actually put his money where his mouth is,” Dr Wollaston said.
The vote on Monday evening is also set to expose divisions among the Labour ranks.
More than 40 Labour MPs said they would go against party policy and support the government.
It is officially opposed to the expansion but leader Jeremy Corbyn has allowed MPs a free vote on a measure that is supported by trade unions.
Some opponents have criticised the scheme on environmental, noise and financial grounds.
Friends of the Earth said it was “morally reprehensible” and would see the enlarged Heathrow emitting as much carbon as the whole of Portugal.