Monday's game was delayed by 20 minutes after fighting between rival fans led to 20 people being injured.
A spokesman for AEK said the club had already lodged an appeal against the fine. Panathinaikos are expected to follow suit.
Another Athens club, Ionikos, have been docked four points and fined 80,000 euros after club president Christos Kanellakis was found guilty of trying to hit a referee after a league game.
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Kanellakis allegedly attempted to punch Theofilos Fotiadis when the duo met at the airport after Ionikos had been beaten 2-0 by Kerkyra.
The Ionikos president was banned from attending games for three years.
Ionikos have appealed against the decision.
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