Unconfirmed reports have alleged that the referee may have used racially-charged language, and he will not officiate this coming weekend as he cooperates with the investigation
The FA had initially received an official complaint from the west London side about the referee on Sunday night, who it says used inappropriate language on two instances during its game against Manchester United.
Unconfirmed reports have suggested that language used towards John Obi Mikel may have been racially charged and the Met have confirmed they will "consider any allegation that is made".
Clattenburg will not officiate any games next weekend while he cooperates with the investigation.
The Society of Black Lawyers have also lodged a complaint with the policing authority to investigate whether a racially-aggravated criminal offence has occurred.
A letter from chairman Peter Herbert to the Metropolitan Police read: "The Society of Black Lawyers wishes to record the incident that took place at Chelsea FC.
"Our information is that racist remarks were directed at John Mikel Obi and at Juan Mata. If so, that is wholly unacceptable in any circumstances.
"Although this matter may be investigated by the FA, it is appropriate that the MPS [Met Police] independently see if a racially-aggravated offence has occurred."