The Metropolitan Police confirmed they had acted on what they described as a "complaint" made by the Society of Black Lawyers after the Blues accused referee Clattenburg of using comments that are understood to have been interpreted as racist remarks at towards John Obi Mikel and Juan Mata at Stamford Bridge on Sunday.
Press Association Sport understands the 37-year-old completely rejects the allegations against him, which are also the subject of an FA investigation.
A police statement read: "An investigation has been launched into alleged comments made during a football match between Chelsea FC and Manchester United FC at Stamford Bridge on 28 October 2012.
"This follows on from a complaint received by the Metropolitan Police Service on 29 October.
"Officers from Hammersmith & Fulham borough are in liaison with Chelsea Football Club and the Football Association.
"At this time, the MPS has not received any complaint from either Chelsea Football Club, or the Football Association.
"We continue to work in partnership with Chelsea Football Club and the Football Association in order to consider any allegation that is made in relation to the reported events."
The police probe came less than 24 hours after the FA launched its own investigation, which it must now decide whether to continue or postpone until after potential criminal proceedings are concluded.
The game's governing body came under fire for the way the John Terry case was allowed to drag out and will be desperate to avoid a similar saga with Clattenburg.
It is understood the referee had yet to be interviewed by the FA this morning but was ready to formally deny any wrongdoing having vowed to co-operate fully with any investigation.
He was said today to be shocked and angered at the allegations made against him and confident of clearing his name.
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