Sheffield Wednesday is investigating after an image was shared online of two of its supporters mocking Bradley Lowery, who died of cancer aged six.
The photograph was allegedly taken at Hillsborough on Friday as the team played Sunderland, who Bradley was a mascot for before he died in 2017.
The club said it would investigate along with South Yorkshire Police.
"We roundly condemn this outrageous and utterly deplorable behaviour," a spokesman said.
"We can only apologise for the undoubted distress caused to Bradley's family and friends."
South Yorkshire Police has been approached for comment.