The federation also fined Trabzonspor more than 3 million Turkish lira ($94,000) on Wednesday.
Turkish police detained 12 people on March 17 after the on-field clashes. Trabzonspor fans charged onto the pitch after the final whistle as Fenerbahce celebrated its 3-2 win in the Black Sea coastal city of Trabzon.
Some Fenerbahce players hit back at the home fans who kicked or punched them, and video of the clashes went viral.
Two Fenerbahce players, Can Egribayat and Jayden Quinn Oosterwolde, were banned for one match.
The incident came just months after the now former president of top-flight club Ankaragucu was arrested for punching a referee following a match, prompting the federation to briefly suspend league games.
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