Three supporters of Zeljeznicar were seriously injured and taken to hospital in Sarajevo, two of them with life-threatening head injuries. Six other supporters were admitted to a hospital in the central town of Travnik.
"One man was operated on and is still in intensive care but stable and conscious for now," Biljana Jandric, a Sarajevo hospital spokeswoman, told Reuters. The other one's life was not at risk, and the third one was released from hospital, she said.
The seven injured police officers were at the Travnik hospital, a spokeswoman for the central Bosnian regional police told Reuters.
Zeljeznicar fans were heading to the northwestern town of Prijedor for the match with Rudar and Borac supporters were on their way to Sarajevo where their club was taking on Olimpik Sarajevo.
Both convoys of supporters were escorted by local police but they could not stop the fight and had to ask for help from special police forces, the police spokeswoman said, adding that several vans were completely destroyed.
Hooligan violence is a common problem in Bosnia, reflecting ethnic divisions still running deep between the Balkan country's Serbs, Croats and Bosniaks (Bosnian Muslims) after the 1992-95 war.
Borac is based in Bosnia's autonomous Serb Republic and Zeljeznicar in the Federation dominated by Bosniaks and Croats. Their fans have a long history of violent clashes.