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.
Olympiakos must play one game behind closed doors after supporters invaded the pitch and attacked some of the Panathinaikos players at the end of their controversial home win in the Athens derby at the weekend.
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.
Some Olympiakos supporters threw punches and kicks at the visiting players and battled with police.
The league also announced that the club would have to pay a fine of €140,000 ($193,100).
Olympiakos president Vangelis Marinakis was fined €15,000 and must stay away from stadiums for two months following inflammatory comments and unsavoury behaviour after the match.
Marinakis has since apologised for his comments which he said were made in the heat of the moment.
Too lenient
Panathinaikos issued a strongly worded statement criticising the punishment as too lenient.
"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."
Panathinaikos claimed their players and officials were locked in the dressing rooms after the match and generally manhandled by local security staff.
Panathinaikos themselves had to play two games behind closed doors in December after fans chased their own team off the pitch and pelted them with missiles folllowing a surprise home defeat.
Saturday's pitch invasion was the fourth in Greece this season as crowd trouble again tarnishes the domestic game.
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