He was taken to Bury police station for questioning and later issued with a fixed penalty charge, he was collected from the station by club officials before the team made the journey back to south Wales.
A spokesman for Greater Manchester Police said: "I can confirm that a Swansea City player was arrested and issued with a fixed penalty charge following an incident at Bury FC.
"The incident took place in the directors' box. The context of the arrest was that there had been a pitch invasion by a substantial number of Swansea fans.
"There was a lot of excited Swansea fans and they got a bit boisterous."
Visiting fans threw missiles at police officers who were trying to clear them from the pitch..
The GMP spokesman said: "Following the conclusion of the match, a pitch invasion took place involving approximately 3,000 fans.
"A short time later, players from the Swansea team appeared in the directors' box, which caused fans to surge towards this area of the ground.
"Due to safety concerns, stewards and police took steps to remove the Swansea players from the box and escort them to the dressing room.
"A member of the Swansea playing staff was issued with a fixed penalty notice for disorder."
A total of nine arrests were made at the match.