UEFA sent the message today in a disciplinary panel ruling to punish disorder at the team's opening match against England.
Russia will be expelled if its fans attack rival fans or stadium security staff at its two remaining Group B matches, or later at Euro 2016 if the team advances.
Russia's "disqualification is suspended until the end of the tournament," UEFA said. "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."
UEFA also fined the Russian soccer federation 150,000 euros (USD 169,000). The charges were for crowd disturbances, fans aiming racial insults at black England players and setting off fireworks during the game.
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UEFA can punish soccer bodies only for the actions of their ticketed fans in and around stadiums.
Russia and England played a 1-1 draw in Marseille on Saturday amid rising tension after several days of clashes between rival fans, French youths and local police.
Though England fans were at the center of the first skirmishes, the violence levels increased when Russian fans arrived closer to the matchday.
Russian fans have caused the worst violence inside stadiums for the second straight European Championship. Among the incidents back in Euro 2012, stadium security staff in Wroclaw, Poland, were assaulted by Russian fans at Russia's opening 4-1 victory over the Czech Republic.
Four years ago, UEFA deferred a punishment of ordering Russia to play three home Euro 2016 qualifying games in empty stadiums. The stadium ban would have been activated if fan violence during qualifying matches was repeated.