"If you tell me that the burka (burqa) is oppressive, then I am with you I would go further and say that it is absolutely ridiculous that people should choose to go around looking like letter boxes," he wrote.
He said businesses and government agencies in the UK should be able to "enforce a dress code" that allowed them to see people's faces.
If a female student turned up at school or at a university lecture looking like a bank robber thenthose in authority should be allowed to converse openly with those that they are being asked to instruct, he wrote.
But 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."
The former Cabinet minister, who had resigned as foreign minister last month amid a clash over the UK's Brexit strategy, said a total ban on face-covering veils would give a boost to radicals and could lead to "a general crackdown on any public symbols of religious affiliation".
However, his remarks prompted calls for an apology, with the Muslim Council of Britain accusing him of "pandering to the far right" and Opposition Labour party MPs accusing him of stoking Islamophobia.
"Our pound-shop Donald Trump is fanning the flames of Islamophobia to propel his grubby electoral ambitions."
Labour's shadow equalities minister, Naz Shah, added: Boris Johnson's latest racist insults cannot be laughed off, like they often are. Theresa May must condemn this blatant Islamophobia and Boris Johnson must apologise.
Another Labour MP, Jess Phillips, said she would report Johnson to the country's Equality and Human Rights Commission (EHRC).
Denmark last week followed France, Austria and Belgium in imposing face-covering burqa and niqab bans in public places and a fine of about EURO 120 has already been imposed on a woman wearing a full-face veil in a shopping centre in the town of Hrsholm.
British Prime Minister Theresa May's official spokesperson 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.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)