The incident is thought to have taken place near the tunnel as the visiting team were walking off the pitch at The New Den.
A club statement read: "Barnsley Football Club and Millwall Football Club are working together, along with The Metropolitan Police to identify a supporter who is accused of racial abuse.
"The incident is alleged to have taken place at the end of the game, from a section of the home crowd. Millwall Football Club have fully cooperated with Barnsley Football Club on this matter and dealt with the allegation in a thorough manner.
"We have no doubt as a club, that the staff at The Den are treating this incident with the severity that is required. Due to the ongoing and potential criminal investigation, Barnsley Football Club will make no further comment at this time."