The president tweeted on Monday that his government will "no longer deal" with Sir Kim Darroch over messages leaked to Britain's Daily Mail, in which the envoy called the Trump White House "inept" and "uniquely dysfunctional".
She also seemingly took a swipe at her likely successor, Boris Johnson, by saying that the country relies on "public servants" who should be able to give "full and frank advice".
With his comments, Hunt waded into the mounting controversy over Darroch's remarks.
And by replacing Darroch, the British government would be playing right into the hands of a leaker, who must have left British diplomats overseas uncertain whether their critical memos about foreign leaders will end up in the newspapers.
"The wacky Ambassador that the UK foisted upon the United States is not someone we are thrilled with, a very stupid guy", Trump added.
During a televised debate Tuesday night, Hunt said "if I am our next prime minister, the ambassador in Washington stays, because it is our decision".
February 2017 - May says Trump's order temporarily banning people from a number of Muslim-majority countries is "wrong" and "divisive".
It led to a scathing tirade from the USA president.
'I think there is a need for reassurance and reflection but the reflection needs to include all of the things the committee is talking about, about how we handle secure information and the systems on which they are transmitted'.
Britain's ambassador to the United States resigned following a tumultuous week of jabs from President Trump after memos he penned - in which he barraged the Trump administration - leaked to British media over the weekend.
She also used that line of defence when Labour MP Justin Madders urged her to tell the two candidates vying her job to ensure the country does not crash out of the European Union without a deal in order for jobs at the Vauxhall manufacturing plant in his constituency to be saved.
Instead, the British opened up a battle with Trump.
In response, Trump said Monday he would "no longer deal with" Darroch, who has served as Britain's ambassador since 2016.
"It's embarrassing that we all know Britain's ambassador believes the United States administration is "dysfunctional, ' 'unpredictable, ' 'faction-riven" and 'inept, '" Peter Ricketts, a former United Kingdom ambassador to France, wrote in an op-ed published in The Guardian Monday.
"It is shameful that Kim Darroch has effectively been forced out for doing the job that diplomats are appointed to do", Scotland's First Minister Nicola Sturgeon tweeted.
However, he was never particularly in favour with Trump himself, who publicly suggested that the then Ukip leader, Nigel Farage, should be May's choice - forcing her spokesman to clarify that: "There is no vacancy".