Daggers defender Gavin Hoyte reported the alleged comment to referee Steve Rushton, who has included the incident in his report to the Football Association.
And a statement from the League Two club, who were holding an anti-racism event on the day of the game, confirmed the Metropolitan Police are now involved.
It read: "Dagenham & Redbridge Football Club wishes to confirm that the case of actual or alleged racist abuse aimed at our defender Gavin Hoyte by an opponent player has been reported to police in the past 24 hours.
"The club will fully support Gavin Hoyte during the investigation and has complete faith in his honesty and integrity.
"Dagenham & Redbridge Football Club wish to reiterate that they have a zero tolerance stance on racism.
"No further statements will be made by the Club on this incident until all investigations have been completed by the appropriate authorities."
Rochdale later issued their own statement in response to the allegations.
It read: "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."