Johnson, who quit the government last month in a dispute over Brexit, wrote in the Daily Telegraph this week that it was "absolutely ridiculous that people should choose to go around looking like letter boxes".
David Lammy, a Labour member of parliament, described Johnson as a "pound-shop Donald Trump" who was "fanning the flames of Islamophobia to propel his own grubby electoral ambitions".
Boris has been accused of Tory Wets of breaching the party's "code of conduct" with his comments.
The party declined to comment on the disciplinary procedure.
Under party rules, complaints that are obviously trivial, lacking in merit or those which cannot fairly be investigated can be dismissed by the head of the investigation.
Pakistani actor Armeena Khan called out former British foreign secretary Boris Johnson over his derogatory comments against women who wear the burqa.
"We need responsibility and action from our politicians, not pandering to the far-right".
Sources close to him have said that he stood by the article in which he argued against a burka ban of the kind adopted by some European countries. By a narrow margin of 48 per cent to 45 per cent they thought he did not need to say sorry for his comments.
Prominent backbench eurosceptic Jacob Rees-Mogg said there was no need for Mr Johnson to apologise.
He told LBC on Wednesday: "No, she's clearly wrong to have asked him to apologise".
Mr Johnson will be given the opportunity to make a statement providing "any evidence or details that will help to establish their position".
The letter, seen exclusively by Sky News, says an apology would be "insufficient" and that Mr Johnson made a "deliberate choice" to "inflame tensions in a way that makes it easier for bigots to justify hate crime against us".
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".