Swansea City say on-loan Liverpool defender Rhys Williams was allegedly racially abused by a home fan towards the end of their 3-3 draw at Luton Town on Saturday.
Williams, 20, was substituted at half-time with the visitors trailing 3-0.
Swansea say an official report was made to match official Tony Harrington and Bedfordshire Police.
They also thanked the force and Luton for for their swift response at the end of the game.
In a statement the Swans said: "Bedfordshire Police has launched a full investigation into the incident. Officers have been to the ground to carry out enquiries and are working with Luton Town to identify the people involved.