Referee Mark Clattenburg is accused of abusing midfielders John Obi Mikel and Juan Mata during Sunday's 3-2 loss to Manchester United in the Premier League, according to the lawyer whose complaint sparked the police investigation.
A day after the globally televised match, Society of Black Lawyers chairman Peter Herbert said he asked officers to look into whether a "racially aggravated offence has occurred" at Stamford Bridge.
The Metropolitan Police responded in a statement on Tuesday by announcing that "an investigation has been launched into alleged comments made during a football match between Chelsea FC and Manchester United FC."
"Officers from Hammersmith & Fulham borough are in liaison with Chelsea Football Club and the Football Association."
Chelsea was only pursuing a complaint against Clattenburg through the English FA.
"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," police said.
Players' union chief executive Gordon Taylor claimed Tuesday that one of Clattenburg's comments was of a "racial" nature.
Clattenburg is yet to respond to the allegations. The Premier League, which authorizes public comment from referees, said he would not make any public statement.
Oriol Romeu has become the first Chelsea player to publicly discuss Sunday's allegations, telling Spanish radio station Cope that Mata told him "there was some problem and he had to stay."
"If there was really a racist comment or something said against a Spanish player, this will be serious," Romeu, an unused substitute in the match, added on Spanish radio station Cope.
The case comes a year after Chelsea captain John Terry was investigated by police after allegations he racially abused an opponent during a league match.
The defender was cleared in court in July of racially abusing Queens Park Rangers defender Anton Ferdinand, but is serving a four-match ban after being subsequently punished by the FA almost a year after the confrontation.
The FA was forced to halt its case when the police probe into Terry started, but English football's governing body will be keen to avoid another high-profile case remaining unresolved for so long.
Officers have not asked the FA to stop its investigation this time.
For the next week at least, Clattenburg won't be refereeing any matches after the referees' body said the "intense level of scrutiny would detract from the match and be unfair to the clubs and the supporters of both sides."
Clattenburg refereed the men's final at the London Olympics in August and is a FIFA candidate to officiate at the 2014 World Cup in Brazil.
Rob Harris can be reached at http://twitter.com/RobHarris