Fans threw flares, litter and a knife onto the pitch and tore down the stadium's security netting at the end of Sunday's match after Konyaspor scored a 90th-minute penalty.
TFF's Professional Football Disciplinary Council said Konyaspor must play their next five home games without supporters and fined them 350,000 Turkish lira ($100,000) for the clashes and for chants made by their fans.
Besiktas were ordered to play one game without supporters, and were handed a 10,000 lira fine. Besiktas Chairman Fikret Orman was fined 30,000 lira and was banned for 45 days for making "unsportsmanlike" statements.
Besiktas play their first home match of the season against Antalyaspor on Sunday. Konyaspor's first home match will be against Ankara side Genclerbirligi on Aug. 21.
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Sunday's violence broke out after supporters of Konyaspor, the main team from Turkey's central Anatolian province of Konya, chanted slogans accusing Besiktas and their fans of links to the outlawed insurgent Kurdistan Workers Party (PKK).
Fans of Besiktas, an Istanbul side whose supporters include a vocal leftist element, responded with a song popular among secular Turks, aimed at the rival fans from Turkey's conservative heartland. The two groups rushed onto the field and fought after the final whistle.
(Reporting by Tuvan Gumrukcu and Dirimcan Barut; Editing by Dominic Evans and Toby Davis)
