Everton are 18th in the Premier League
It took place 15 minutes into Everton's 1-0 defeat to the Gunners at Goodison Park on Sunday.
"Racism has no place in our stadium or our communities," the club said in a statement.
Everton said the reported incident happened in the Lower Gwladys Street Stand near to the Bullens Road Stand.
"Everton condemn all forms of discrimination and we will seek the strongest possible sanctions to tackle anti-social and/or criminal behaviour, including club bans and criminal prosecution," the club's statement added.
In August, Everton said they would support a police investigation into "racist comments" directed towards their Belgium midfielder Amadou Onana.
Earlier that month, the club had condemned the social media abuse suffered by French striker Neal Maupay - now on loan at Brentford - following Everton's 1-0 opening-day home loss to Fulham.
-- Courtesy of BBC Sport