Katidis, 20, a former captain of Greece's under-19 team, made the alleged salute in celebrating his winning goal in a 2-1 Super League victory over lowly Veria late on Saturday.
"The player's action to salute to spectators in a Nazi manner is a severe provocation, insults all the victims of Nazi bestiality and injures the deeply pacifist and human character of the game," EPO said in statement.
Katidis was heavily criticised by political parties and fans on Twitter and Facebook following the incident at the Athens Olympic Stadium. Sunday marks the 70th anniversary of Greek Jew deportations in Nazi concentration camps in the Second World War.
AEK have asked Katidis to explain himself and will then decide his future at a board meeting next week.
Katidis denied he gave a Nazi salute. "I am not a fascist and would not have done it if I had known what it meant," Katidis said on his Twitter account.
The player said he was simply pointing at Michalis Pavlis in the stands to dedicate the goal to his team mate as he continues to fight health problems.
AEK's German coach Ewald Lienen backed Katidis.
"He is a young kid who does not have any political ideas. He most likely saw such a salute on the Internet or somewhere else and did it without knowing what it means," he said.
AEK are languishing in 10th place in the table with 29 points from 26 games. Veria are fourth from bottom.
Katidis joined the club from Aris Salonika last year after impressing in Greece's run to the final of the European Under-19 Championship where they lost to Spain.
