It is understood that the process is being triggered automatically after the receipt of a number of complaints over the former foreign secretary's comparison of Muslim women in face-covering veils with bank robbers or letter boxes.
The former foreign secretary has been blasted by members of his own party and the opposition over comments he made in his Daily Telegraph column.
But Muslim organisations said there had been "a real impact" from Johnson's remarks.
The Conservative Party's announcement on Thursday that Mr Johnson would face an inquiry has provoked a furious war of words, with many Tories regarding the move as an over-reaction.
Comedian Rowan Atkinson, best known for his roles in Blackadder, Mr. Bean and Johnny English, has defended Johnson.
And he added: "All jokes about religion cause offence, so it's pointless apologising for them.
I fear an eruption of anger amongst our party's core voters and grassroots activities if this obsessive political correctness doesn't stop".
Get ready for another white nationalist rally -- and counter-protests, too
In a news conference on Thursday, D.C. police said the Unite the Right rally is something they have been planning for months. No rally has been scheduled for Charlottesville this year because the city refused to issue a permit.
"You should really only apologize for a bad joke".
"Unfortunately under the new code of conduct, if a formal complaint is lodged - and I believe that reports say Lord Sheikh, a Conservative peer, has lodged a formal complaint - it has to be investigated".
Mr Mitchell, who was chief whip in 2012 and global development secretary before that, told BBC Two's Newsnight: "I don't think he should apologise. On that basis, no apology is required".
"This is quite an important issue about free speech and it's got nothing to do with the terrible events that take place over Enoch Powell and the Rivers of Blood speech".
'Full bandwagon jumping territory'Conor Burns, Tory MP for Bournemouth West'It's bash Boris'Andrew Bridgen, Tory MP for North West Leicestershire " This [inquiry is] being use to try and discredit Boris Johnson from people who are anxious about him in inside the Conservative party and outside the Conservative party.
Johnson's comments followed Denmark introducing a ban on burqas in public places.
Critics from inside and outside the Conservative party, including Prime Minister Theresa May, have called on Johnson to apologise.
Mr Johnson, who is holidaying overseas, has made no response to demands for an apology.