But Mr Johnson has refused to back down, with friends claiming it is "ridiculous" to criticise his comments and accusing party chiefs of "shutting down the debate". "It's not language I would have used and I think he was wrong to have used that language, and I agree with Brandon Lewis".
Former attorney general Dominic Grieve said he would quit the party if Mr Johnson became leader after an article in which the former foreign secretary described women wearing a face veil as "looking like letter boxes".
Sayeeda Warsi, a former foreign minister under David Cameron and Conservative Party Chairman - who has always been a critic of Islamophobia within the party - said this week that Muslim women "should not be a political football to increase your popularity ratings amongst the Tory faithful".
A panel of at least three people, appointed by Mr Lewis, will include one independent member, one representative of the voluntary party and one nominated by the chair of the backbench 1922 Committee. Possible action "includes suspension of membership or expulsion from the party among other things", says the BBC.
And an imam who has previously criticised the burka said Mr Johnson should not "apologise for telling the truth".
However, from his words, Sam Johnson not going to give up, writes BusinessInsider.
Johnson, who is now on holiday, has refused to apologize for his controversial descriptions despite calls to do so by the Tory party hierarchy. The person in the niqab "is similar to a Bank robber" or "Inbox".
May was "perhaps relieved she no longer has to bite her tongue when asked about her erstwhile cabinet colleague", says The Times.
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Ex-Ukip leader Nigel Farage said: 'Public figures should be able to say what they really think without constant demands to apologise.
Bannon, a former White House chief strategist, praised Johnson in several interviews during a visit to the United Kingdom last month, and also met privately with the former foreign minister, according to Buzzfeed News. "If we fail to speak up for liberal values then we are simply yielding ground to reactionaries and extremists".
Sayeeda Warsi, a Conservative member of the House of Lords, said Johnson was using Muslim women as a "convenient political football to try and increase his poll ratings".
"I hope he will be disciplined but I'm not holding my breath".
But it's also "impossible to ignore the fact that pretty much all the senior Tories who have criticised Johnson so far" voted Remain in the European Union referendum and that those lining up to defend him "are largely Brexiteers", says Politico.
The backlash against Mr Johnson began when his former deputy at the Foreign Office, minister Alistair Burt, said he would never have made such comments and argued that there was "a degree of offence" in them.
That makes it "hard to see this row other than through the prism of a much bigger dispute about the direction in which the Conservative Party, and the country, are headed this autumn", the news site adds.