The disciplinary committee of the Turkish Football Federation (TFF) said Trabzonspor would also have to pay a 915,000 Turkish lira ($320,000) fine.
The referee called a halt to the game on April 24 in the 88th minute when a fan, apparently supporting Trabzonspor, attacked an assistant referee and other supporters invaded the pitch.
The assistant referee was pinned to the ground and kicked by the fan, who was detained, pictures showed.
Fenerbahce, contenders for the Super Lig title, had been leading 4-0 at the time and were subsequently awarded the tie by the same score.
Trabzonspor and Fenerbahce fans have a long history of enmity and in April last year Fenerbahce's team bus was shot at as the players were travelling in the Trabzon region, seriously wounding the driver.
Fans of Trabzonspor have a reputation for volatility, seeing their team as victims of domination by the big Istanbul sides.
The Turkish football authorities have long waged a battle against crowd trouble, introducing a hugely controversial identity card system for fans to attend games.