The incident occurred during Saturday's 2-1 win over Dale which saw the Daggers grab a late winner.
A statement on the Dagenham website said Hoyte reported the incident to match referee Steve Rushton, who later informed the Football Association.
"Dagenham & Redbridge Football Club wish to reiterate that they have a zero tolerance stance on racism," it said.
"The club will fully support Gavin during the investigation and has complete faith in his honesty and integrity.
"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."
Rochdale confirmed they were aware of the allegation and confirmed they would co-operate with Football Association and police inquiries as well as opening their own investigation.
"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," a statement on the Dale website said.
"Rochdale Football Club reiterates its commitment to fully co-operating with the Football Association and the Metropolitan Police."