Johnson was called upon to apologise but declined, according to his employers. He is believed to be on vacation.
Critics said it was outrageous that a Conservative aspirant to top office and Britain's former face to the world would launch such a broadside against traditional Islamic attire.
The streets of London are filled with women sporting face veils, some of them visitors to pricey shopping districts, others British citizens. About 5 per cent of the British population is Muslim, mostly from Pakistan and Bangladesh.
David Lammy, a member of the opposition Labour Party, called Johnson a dime-store version of US President Donald Trump and said he was "fanning the flames of Islamophobia" for political gain.
May said his words "clearly caused offence ... and I do think that we all have to be very careful about the language and terms we use."
Culture Secretary Jeremy Wright said that while it was reasonable to have "a robust conversation" about the wearing of veils, he didn't like Johnson's tone. "We're not talking to our friends in the pub; we are public figures, and we have an additional obligation to be careful," Wright told the BBC.