Europe’s governing body declared Russia responsible for the stadium disturbances, racist chanting and fireworks thrown during the Russia-England game in Marseille on Saturday.
It ordered the “suspended disqualification” of the team and fined the Russian Football Union 150,000 euros ($170,000).
“This disqualification is suspended until the end of the tournament,” said the UEFA disciplinary commission decision.
“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.
UEFA stressed that its order only applied to trouble inside stadiums where the governing body is responsible for security.
Russia are playing Slovakia in Lille on Wednesday, sparking fears its fans will come into contact with English fans whose team is playing Wales in nearby Lens on Thursday.
After the 1-1 draw in Marseille, Russian fans crossed security barriers inside the Stade Velodrome and attacked England fans. Dozens of English supporters, including women and children, had to flee across security barriers to escape.
UEFA had already warned Russia and England that it could disqualify them if there was more trouble. But only Russia was charged over the conduct of its fans.