Tory officials opened the inquiry into the former foreign secretary after receiving complaints about his widely-criticised remarks.
The probe could, in theory, lead to the MP being expelled from the party, although such an outcome appears highly unlikely.
Mr Johnson caused outrage after calling the Muslim niqab veil “absolutely ridiculous” and suggesting women who wear it look like “letterboxes” and “a bank robber”.
Several senior Conservatives have called for action to be taken against him, with some demanding he have the party whip removed.
Theresa May and Brandon Lewis, the Conservative Party chairman, and Scottish Conservative leader Ruth Davidson have all called on Mr Johnson to apologise for the comments.
He has so far refused to do so, with allies insisting the criticism of his comments was “ridiculous”.
The probe will investigate whether Mr Johnson breached the party’s code of conduct, which says members must “lead by example to encourage and foster respect and tolerance”.
It will initially focus on collecting evidence and statements to determine whether the inquiry should proceed. Mr Johnson will be given the opportunity to provide a statement outlining “any evidence or details that will help establish their position”.
If there is deemed to be enough evidence of a breach of rules, a disciplinary panel consisting of at least three people will be appointed by Mr Lewis. Graham Brady, the chair of the 1922 committee of Tory MPs, will select one member.
The panel will determine whether Mr Johnson broke any rules and pass its conclusions to Ms May and the Conservative Party board, who will decide what punishment, if any, he should face.
Two Tory peers are among those who have called for disciplinary action to be taken against Mr Johnson.
Lord Sheikh, the founder of the Conservative Muslim Forum, said he had written to Mr Lewis calling for “severe action” and suggesting the whip be removed from the former foreign secretary.
Baroness Warsi, a former co-chair of the party, called Mr Johnson’s comments “reprehensible” and said there should be “real action” and “consequences” if he refuses to apologise.
As well as the complaints made to the Conservatives, Mr Johnson has also been reported to the police and to the Equalities and Human Rights Commission.