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.
Johnson, who leaped back into contention to replace Theresa May as prime minister after resigning his post in protest against the government's Brexit plan, made the controversial comments in a newspaper column on Monday.
However, the panel would be appointed by Chairman of the Conservative Party Brandon Lewis who was one of the first people to demand Johnson to apologise, raising questions of how such an investigation could be fair.
"In his recent comments Boris Johnson further fuels Islamophobic sentiments by comparing women who wear burkas to letterboxes and bank robbers". Johnson added: "If a constituent came to my MP's surgery with her face obscured, I should feel fully entitled - like Jack Straw - to ask her to remove it so that I could talk to her properly.
We must not fall into the trap of shutting down the debate on hard issues", a source close to Johnson told reporters.
"Yet another privileged middle-aged bloke telling women what they can and can't wear".More news: Space Force will be sixth branch of United States military, Pence says
Lord Sheikh, the founder of the Conservative Muslim Forum, said an apology would not be enough and said Mr Johnson should be stripped of the Tory whip.
Amid calls to apologise for his remarks, a former United States diplomat, and foreign policy adviser, Jim Jatras, has claimed President Donald Trump would spark similar fury if he made similar remarks.
Some suspected Johnson's burka comments were meant to boost his appeal among right-wing members of the party.
Mr Johnson made the remarks in a Daily Telegraph column.
"These were offensive comments but clever politics", she said.
"As an organisation championing the rights of Muslim women, we are all too familiar with the ways in which this "natural reaction" manifests itself: a woman who was attacked, punched and had her headscarf ripped off, and another who had a bottle smashed over her head in a bus, both in Glasgow this year".