The violence left at least 20 people hospitalized in the French port city of Marseille.
There were also clashes in the stadium following England’s 1-1 Euro 2016 draw with Russia, after Russia fans appeared to rush at England supporters, according to AP news agency.
Several arrests also made during the clashes.
After the final whistle of the match at the Stade Velodrome, Russian supporters were seen storming a section of the ground housing England fans, causing them to flee. Video footage and still images posted on social media also showed people running towards one side of the stadium in order to escape.
The Russian team could now face an anxious wait after the crowd trouble. Four years ago Russia was sanctioned and handed a suspended six-point deduction following crowd trouble in Poland at Euro 2012.
Witnesses said trouble began in the stadium after flares were let off by Russian fans near the end of the game. Some fans had then climbed across barriers designed to keep rival fans apart.