"If you say that it is weird and bullying to expect women to cover their faces, then I totally agree", Johnson said.
Party chairman Brandon Lewis will nominate two members of the panel, and because the complaint is about a member of Parliament, a third will be nominated by Graham Brady, the chairman of the party's backbench 1922 committee.
Mr Johnson will be given the opportunity to make a statement providing "any evidence or details that will help to establish their position".
Johnson asserted that schools should be entitled to tell students to remove a veil if one "turns up ... looking like a bank robber".
Johnson labelled Muslim dress "oppressive", and claimed of the niqab: "It is absolutely ridiculous that people should choose to go around looking like letter boxes".
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"I think Boris Johnson used language in describing people's appearance that has obviously caused offence", she said.
'For this reason Britain must emulate France, Belgium, Austria, Bulgaria and Denmark in banning the burka'.
Anti-hate crime groups said the comments by Johnson, who resigned last month, would encourage Islamophobic and sexist abuse at a time when attacks were already on the rise.
Scotland Yard chief Cressida Dick said the comments did not amount to a hate crime and police have not received any criminal complaint against Mr Johnson.
Johnson has so far refused requests to apologise for the comments.
Others have suggested Johnson could be positioning himself as a candidate attractive to anti-immigrant, right-wing, anti-European voters who have previously voted for the United Kingdom Independence Party (UKIP), noting his contact with Steve Bannon, the controversial former adviser to US President Donald Trump. "We have to call it out".
According to the BBC, Johnson's supporters defended his remarks, saying that he was simply sticking up for "liberal values". Both sides of the Tory party are gunning for the other - and "this will be a fight to the death".