The 30-year-old man collapsed inside the Britannia Stadium on Saturday just after the half-time interval in the game between Stoke and Blackburn Rovers.
Police said they were investigating what led to the man's death and would not comment on a BBC report that he had been hit on the head with a bin.
"The circumstances are being fully investigated and a 25-year-old man remains in custody and is helping police with their inquiries," Staffordshire Police said.
Chief Inspector Adrian Roberts, who was in charge of policing at the game, told the BBC that no Stoke fans were involved in the incident.
Some 1,300 Blackburn fans were at the game, which Stoke won 3-0.
Police and paramedics found the man, a Blackburn supporter, on a concourse inside the stadium with other Blackburn fans.
He received medical treatment inside the stadium before being taken to hospital where he died early on Sunday.
