Police spokesman Andreas Angelides said on Wednesday that nine fans and six police officers were also injured during the incident. The violence occurred along a highway leading to the capital Nicosia, shortly before APOEL Nicosia played AEL Limassol on Tuesday.
Angelides said police used tear gas to disperse fights involving several dozen fans, while nine people have so far been arrested. Three cars were also damaged.
APOEL beat AEL 3-0 to take top spot on goal difference, with five matches remaining in the play-off round.