Former foreign secretary Mr Johnson has caused outrage with a newspaper article comparing women in the face-covering veils to bank robbers, with Conservative Party chairman Brandon Lewis ordering him to apologise for the remarks.
David Lammy, a Labour MP, wrote on Twitter: "Muslim women are having their burkas pulled off by thugs in our streets & 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".
Culture Secretary Jeremy Wright joined the chorus of criticism and former Cabinet minister Lord Pickles said that, while it would be a "very big leap" to suggest Mr Johnson could be thrown out of the party, "you never know how these things develop".
Mr Johnson is likely to be a contender to replace her.
"I would go further and say that it is absolutely ridiculous that people should choose to go around looking like letter boxes".
Fiyaz Mughal, the founder of Tell MAMA UK, which campaigns against anti-Muslim violence, said Johnson's comments "clearly" amounted to Islamophobia.
Ms May said she agreed with Mr Lewis.
Boris Johnson has stood by his remarks about the burka after the Conservative Party chairman told him to apologise.
Daily Star Online contacted the Tories to ask what will happen in Johnson fails to say sorry.
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Since he resigned in protest at May's Brexit plans last month, Johnson has been touted as a potential prime minister by those in the Conservative Party who want a harder departure from the European Union.
"It is Islamophobia and I think it's pretty outrageous".
His article stated that there was no requirement in the Koran for women to cover their faces, and attacked "bullying (and) oppressive" male-dominated governments which tried to force them to do so.
He noted there had been no follow up to his June meeting with party members over complaints of anti-Muslim incidents.
Conservative MP Nadine Dorries backed a ban on the burka, saying: "Any clothing a woman is forced to wear which hides both her beauty and her bruises should be banned and have no place in our liberal, progressive country".
The Bookmarks bookshop in Bloomsbury, central London, said that "around a dozen mask-wearing fascists" attempted to intimidate staff and customers and to destroy books and other materials on Saturday.
"The Anti-Nazi League was an iconic movement over several decades that successfully combated the far right through the mass mobilisation of trade unionists and anti-racist campaigners".
She also refused to say if she thought the comments were Islamophobic - as Scottish First Minister Nicola Sturgeon said they were.