Cardiff and Swansea have condemned a video circulating on social media and containing racist language apparently aimed at Republic of Ireland forward Michael Obafemi from the fixture between the two clubs on 2 April.
The footage appears to show a Cardiff fan inside the stadium using a racial slur at Swansea forward Obafemi, who scored twice in the visitors' 4-0 South Wales derby win.
Cardiff have reported the matter to South Wales Police and discussed the video with anti-discrimination group Kick It Out.
"Cardiff City have spoken at length with Kick It Out on the matter, have passed evidence on to South Wales Police and will fully support their investigations," the Sky Bet Championship club said in a statement.
"The club is disgusted by the deplorable, stomach-churning language and stands by football's commitment to stamping out such abhorrent behaviour.
"There is no place for it in our sport or society."
South Wales Police has confirmed the matter is being investigated.
A statement from the force said: "South Wales Police is aware of footage circulating on social media from Cardiff City's home fixture against Swansea City at The Cardiff City Stadium on April 2.
"Enquiries are ongoing. Anyone with information, or the individual himself, is urged to contact South Wales Police quoting occurrence *140557."
Obafemi's Swansea colleague Joel Latibeaudiere shared the video on his Twitter account and said: "Disgraceful, @CardiffCityFC should ban this fan immediately.
"Social networks do nothing online, but this is someone who's easily identified. Ban him!"
Latibeaudiere accompanied his post with the hashtag 'NoRoomForRacism'.
Swansea players both past and present have been the subject of racial abuse.
Last year Swansea were the first EFL club to boycott social media during a seven-day protest against online abuse.
A club statement said: "Swansea City Football Club is aware of a video circulating on social media from the fixture against Cardiff City on April 2.
"We wholly condemn the abhorrent language used and we are actively working with South Wales Police and Cardiff City with their enquiries.
"There is no place for such behaviour in society, let alone football, and as a club we will unequivocally support our players and staff to help eradicate all forms of discrimination from the game."