A statement from the npower League Two club said the alleged incident involved Dagenham defender Gavin Hoyte and an unnamed Rochdale player during Saturday's match between the sides. Hoyte also reported it to match referee Steve Rushton.
In their statement, Dagenham also said that Rushton had informed the Football Association of the allegation.
Dagenham added: "The game against Rochdale was championed as a 'Daggers Against Racism Family Fun Day' and it is deeply disappointing that this incident has tarnished the day.
"The club will fully support Gavin Hoyte during the investigation and has complete faith in his honesty and integrity."A Scotland Yard spokesman said: "We can confirm that we have received an allegation of racial abuse in relation to the football match between Dagenham and Redbridge and Rochdale that took place on Saturday, January 12."
(reopens) Rochdale confirmed they would co-operate with Football Association and police inquiries as well as opening their own investigation.
A statement from the club read: "Rochdale Football Club have today been contacted by Dagenham & Redbridge Football Club regarding an alleged racist comment made by a Rochdale player towards their player Gavin Hoyte during yesterday's League Two encounter.
"Both Rochdale Football Club and Dagenham & Redbridge Football Club enjoy an excellent relationship and Rochdale Football Club are grateful to Dagenham & Redbridge for contacting us on this matter.
"We are aware that the matter has been reported to the Metropolitan Police and the Football Association and we will fully co-operate with both authorities on this matter as well as investigating it internally.
"Rochdale Football Club has a zero tolerance against racism and fully supported the Daggers Against Racism Family Fun Day, as well as our on-going support of the Kick Racism Out of Football campaign, where as a club our players have worn the anti-racism T-shirts on at least three occasions this season, including on Saturday.
"We also share the disappointment of our friends at Dagenham & Redbridge that such an accusation has occurred on a day when both clubs were supporting an anti-racism day."