Police said the man is being held for an alleged breach of the peace and is expected to appear at Glasgow Sheriff Court today.
Celtic chief executive Peter Lawwell told the club's website: "Clearly, Celtic take this issue extremely seriously and it is satisfying that this individual has been identified so swiftly. The individual in question has now been banned for life from attending Celtic matches, both home and away.
"Outwith this incident, the Celtic support was phenomenal. It should also be said that Gordon [Strachan] and his team deserve enormous praise for achieving one of the most famous results in the club's history, against the champions of Europe."