The prime minister and his wife Carrie wanted to construct the outdoor structure for their son Wilf in autumn 2020, a few months after he was born, it is claimed.
However, Mr Johnson’s close protection officers are said to have raised concerns it would be visible from the road and could be a potential security risk.
The couple decided against the project following police advice, The Times reports. It is not certain permission would have been given to build the treehouse because a lot of the trees on the estate are protected.
The exact details of the plans are not known but luxury playhouses can have a range of features including zip wires, rope bridges and even hot tubs.
The bulletproof glass on Wilf’s unbuilt treehouse significantly added to the cost of the project, it was reported.
Blue Forest, a luxury treehouse designer, told the newspaper that its playhouses for children start at £90,000 and go up to “whatever you want to pay”.
Mr Johnson refused to discuss the claims during an interview with journalists travelling with him in Rwanda, where he is attending a Commonwealth leaders summit.
“I’m not going to comment on non-existent objects or non-existent jobs to do with my family,” he said.
A government spokesman added: “We do not comment on private or family matters which do not involve any ministerial declarations or taxpayer funds.”
The details come as Mr Johnson continues to fight for his political life after two damaging by-election losses and the resignation of Conservative Party chairman Oliver Dowden.
Mr Dowden said he and Tory supporters were “distressed and disappointed by recent events”, telling Mr Johnson that “someone must take responsibility”.
On Thursday the Tories lost their former stronghold of Tiverton and Honiton to the Liberal Democrats and Wakefield to Labour.
Despite being under immense pressure Mr Johnson came out fighting on Saturday and insisted he is not going to undergo any “psychological transformation”.
He said he must “humbly and sincerely” accept any criticism he receives in his job, but argued every government gets “buffeted” by bad by-election results mid-term.
Put to him that Mr Dowden had resigned as Conservative chair saying business could not continue as usual, Mr Johnson told BBC Radio 4’s Today programme: “If you’re saying you want me to undergo some sort of psychological transformation, I think that our listeners would know that is not going to happen.
“What you can do, and what the government should do, and what I want to do, is to get on with changing and reforming and improving our systems and our economy.”