The Besiktas and Galatasaray fans were detained on Monday after police examined footage from Sunday evening's basketball game, which had to be called off as hooligans shouted obscenities and sprayed fire extinguishers at each other.
Besiktas and Galatasaray have been fierce rivals in football, Turkey's most popular sport, for more than a century.
Their fans, along with supporters of Fenerbahce, another of the country's biggest clubs, are not allowed to attend away games between the teams in soccer and basketball.
The regulation, however, does not apply to other sports, including wheelchair basketball.
"Besiktas supporters should not have been allowed into the stands. Who will pay the price for the injured athletes and supporters," Sedat Incesu, coach of the Galatasaray wheelchair basketball team, told the NTV television station.
"If hooligans are now seen in wheelchair basketball stands then we have nothing else to say, it is over ... Sports are now officially dead in this country," he said.
Police used tear gas to break up the brawl at the Ahmet Comert Sports Hall in Istanbul. Television images showed basketball players covering their faces with their jerseys as officers in riot gear led basketball supporters to safety.
A court invasion had already caused a half-hour delay before the game started, and Galatasaray was leading 31-26 when play was suspended, six minutes from the end of the second quarter.
Galatasaray are one of Europe's top wheelchair basketball teams, and have won three European Champions Cup titles in the last four years.