Russia could be thrown out of Euro 2016 if their fans cause further trouble inside a stadium after the UEFA imposed a suspended disqualification and a 150,000 euro (119,066.15 pounds) fine on the Russian Football Union (RFU) on Tuesday.
Masked Russia supporters charged at England fans, punching and kicking them, after the final whistle of the 1-1 Group B draw at the Stade Velodrome in Marseille on Saturday.
Russia's fans were also involved in violent clashes with England supporters in the port city before and after the match.
"Charges relating to crowd disturbances, use of fireworks and racist behaviour had been brought against the RFU (Russian Football Union)," UEFA said in a statement, adding its ethics committee had imposed a suspended disqualification and fine.
"Such suspension will be lifted if incidents of a similar nature (crowd disturbances) happen inside the stadium at any of the remaining matches of the Russian team during the tournament," it added.
The violence in the stadium followed three days of clashes between English, Russian and French fans in the Mediterranean port city that drew a strong response from riot police.
French Prime Minister Manuel Valls said on Tuesday that some football fans will be deported from France after violent clashes marred the start of the Euro 2016 tournament, and a group of Russia fans was detained near Cannes on the French Riviera.