Olympiakos captain Vasilis Torosidis has also been given a five-game ban by the Greek Super League following his sending off for headbutting midfielder Sebastian Leto in the closing stages of Saturday's game at the Georgios Karaiskakis stadium.
The punishments were handed down on Thursday after hundreds of fans invaded the pitch following the league leaders' tempestuous 2-1 win that took them 10 points clear of their local rivals with just seven matches to play.
"This decision is a challenge for the public sense of justice. It shows, if anything, in the most eloquent way, that this mode of institutional organisation and football is so wrong that it should change tomorrow," the club said.
"The imbalance of what they (Olympiakos supporters and officials) did - the pitch invasion and the use of force against players and the bullying in the changing rooms - compared to the penalty imposed has left us speechless.
"It is now clear that changes must be made at all levels in Greek football and these changes must be both direct and sweeping."
Saturday's pitch invasion was the fourth in Greece this season as crowd trouble again tarnishes the domestic game.
