Trump confirmed late Thursday that he canceled his trip to cut the ribbon at the new USA embassy, saying that he is "not a big fan" of an Obama-era real estate sale involving the new site.
Mr Trump also criticised the location of the new building in Vauxhall, south London, as an "off location", adding: "Wanted me to cut ribbon-NO!"
Claire Treacy, a spokeswoman for the museum, told The Washington Post that they chose to move the wax Trump after learning that the president had canceled his trip.
The decision to move from the former prestigious location in Mayfair, central London, was taken by the administration of former Republican president George W. Bush in October 2008, partly for security reasons in the wake of the September 11, 2001, attacks.
A Trump visit has been on the cards since British Prime Minister Theresa May visited the United States a few days after Trump's inauguration a year ago.
But Trump's late-night tweet singled out problems with the handling of the embassy.
However, London's mayor Sadiq Khan, who has been a target of Mr Trump's twitter tirades, said the president had "got the message" that he was not welcome in the United Kingdom capital.
In a BBC interview on Sunday, May insisted that Trump "will be coming to this country" in spite of the opposition.
"His visit next month would, without doubt, have been met by mass peaceful protests", he added.
But Johnson accused Khan and Labour leader Jeremy Corbyn of damaging US-UK relations with their vocal criticism.
"We will not allow US-UK relations to be endangered by some puffed-up, pompous popinjay in City Hall", Johnson tweeted.
A spokesman for her Downing Street office said Friday said that the state visit plans have not changed, although no date has yet been set.Opposition to Trump's visit was initially focused on his travel ban on Muslim-majority countries, and most recently his re-tweet of anti-Muslim videos posted by a far-right organization, Britain First.
"The US is one of our oldest and most valued allies and our strong and deep partnership will endure", the spokesman said.
Almost two million British people added their names to an online petition in 2017 calling for Trump's visit to be downgraded from a state visit to avoid embarrassing the queen.
"Our new embassy reflects not just America's special history with the United Kingdom but the special future ahead of us as we advance the prosperity and security of both our nations", he wrote.
The area became known as "Little America" at the time.
The new building will open for business on January 16.
The cancellation of the visit was "excellent news", said Lindsey German, organizer of the Stop the War Coalition, which had planned a large protest against Trump.