(Reuters) - At least one other person was being treated in hospital for his injuries, the state-run Anatolian news agency reported.
Thousands of Besiktas fans threw rocks and bottles to break through a police cordon and attack some 1,200 Bursaspor supporters, CNN Turk said.
The channel showed footage of police using batons and tear gas to break up the skirmishes outside Besiktas's Inonu Stadium.
Bursaspor fans blame Besiktas for their side's relegation to the second division in 2003 after the Istanbul club played badly against another team facing possible relegation.
Since then, encounters between the fans have often led to violence.
Sunday's game ended in a 1-0 win for 13-times champions Besiktas.
(Writing by Ayla Jean Yackley; Editing by Clare Fallon)