A statement from the club said that the alleged incident involved Dagenham defender Gavin Hoyte and an unnamed Rochdale player during yesterday’s match between the sides.
Hoyte also reported it to match referee Steve Rushton.
In addition, Dagenham’s statement also revealed that Rushton had informed the Football Association of the allegation.
A club spokesperson 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.”