The brawl between the fans took place before and after the game Saturday, forcing police in riot gear to fire tear gas to disperse crowds. The fans also hurled bottles and other objects at officers.
After the game, Russian fans attacked the section where British fans were sitting. Panicked fans fled from the scene of brawl as the streets got filled with smoke.
Mathieu Duroselle, a spokesman for Marseille police, said at least 31 people were injured in the clashes. He added that the number included three officers who got slightly injured.
On the field, Russia played out a 1-1 draw against England. French police arrested at least 17 people over two days.
"About 1,000 police officers were deployed to secure the game," Duroselle said. "The situation seems calm now by the stadium and it seems like bars are closed."
The Union of European Football Associations said an announcement regarding disciplinary proceedings will be made on Sunday.
"People engaging in such violent acts have no place in football," said the UEFA, the administrative body for association football in Europe.