The former foreign secretary came out against calls for a ban on the face-covering veils in public places, but described them as “absolutely ridiculous” and compared their wearers to rebellious teenagers.
His comments, in response to the introduction of a burka ban in Denmark, sparked an angry response from Muslim organisations and MPs, who accused him of stoking Islamophobia for political gain.
The assistant secretary general of the Muslim Council of Britain, Miqdaad Versi, said Mr Johnson was “pandering to the far-right”, while Labour MP David Lammy branded him a “pound-shop Donald Trump”.
Labour’s Jess Phillips said she would report Mr Johnson to the Equality and Human Rights Commission.
Denmark last week followed France, Germany, Austria and Belgium in banning face-covering garments like the burka and niqab in public places.
A fine of around £120 has already been imposed on a woman wearing a niqab in a shopping centre in the town of Horsholm, after another woman reportedly tried to tear it off.
Downing Street confirmed that the Government does not support a ban in the UK.
Writing in the Daily Telegraph, Mr Johnson said he felt “fully entitled” to expect women to remove face coverings when talking to him at his MP’s surgery, and said schools and universities should be able to take the same approach if a student “turns up ... looking like a bank robber”.
“If you tell me that the burka is oppressive, then I am with you,” he wrote.
“If you say that it is weird and bullying to expect women to cover their faces, then I totally agree - and I would add that I can find no scriptural authority for the practice in the Koran.
“I would go further and say that it is absolutely ridiculous that people should choose to go around looking like letter boxes.”
Businesses and government agencies should also be able to “enforce a dress code that enables their employees to interact with customers”, including by allowing them to see their faces, said Mr Johnson.
But he added: “Such restrictions are not quite the same as telling a free-born adult woman what she may or may not wear, in a public place, when she is simply minding her own business.”
A total ban would give a boost to radicals who claim there is a “clash of civilisations” between Islam and the West, fanning the flames of grievance and turning women into “martyrs”, he warned.
And he said that a ban on burkas could lead to “a general crackdown on any public symbols of religious affiliation”.
Mr Johnson wrote: “Like a parent confronted by a rebellious teenager determined to wear a spike through her tongue, or a bolt through her nose, you run the risk that, by your heavy-handed attempt to ban what you see as a bizarre and unattractive adornment, you simply stiffen resistance...
“If Danish women really want to cover their faces, then it seems a bit extreme - all the caveats above understood - to stop them under all circumstances. I don’t propose we follow suit. A total ban is not the answer.”
Mr Versi responded on Twitter: “Boris Johnson says a woman in niqab is ‘looking like a bank robber’ or ‘looking like letter boxes’.
“Is this language anything other than pandering to the far-right? Deeply disappointing that (the) Telegraph platforms this disgusting language.”
And Mr Lammy said: “Muslim women are having their burkas pulled off by thugs in our streets and Boris Johnson’s response is to mock them for ‘looking like letter boxes’.
“Our pound-shop Donald Trump is fanning the flames of Islamophobia to propel his grubby electoral ambitions.”
Labour MP Stella Creasy said voters in a potential Conservative leadership contest should note that Mr Johnson appeared to be positioning himself as a figure in the mould of US right-winger and former Trump aide Steve Bannon.
She warned he was in danger of “going full Morrissey”, in reference to the singer who has been mired in controversy over comments on immigration, and said her advice to Mr Johnson was that “being a buffoon, not being a racist and misogynist, (is) more British”.
Prime Minister Theresa May’s official spokesman said: “The long-standing Government position on this is clear, that we do not support a ban on the wearing of the veil in public.
“Such a prescriptive approach would be not in keeping with British values of religious tolerance and gender equality.”