The Russian Football Union was fined 30,000 Swiss Francs (30,000 dollars) by FIFA on Tuesday for "discriminatory chants" by fans during Russia's home friendly with France in March.
The announcement, made by world football's governing body FIFA in a statement, comes just weeks before Russia holds the World Cup for the first time.
Media reports said monkey noises were directed at France players such as Paul Pogba. The stadium in St. Petersburg will host various World Cup games in June and July including a semi-final.
"The FIFA Disciplinary Committee... after analysing all the specific circumstances of the case, in particular the gravity of the incident but also the limited number of fans involved, decided that the Russian Football Union was liable," the statement said.
"At its tournaments, including the 2018 FIFA World Cup, FIFA has also introduced a three-step procedure in case of discriminatory incidents, which allows referees to actively intervene to make the discriminatory behaviour stop."
Referees have the authority to first stop the match and request a public announcement to try to end the chanting. They can then suspend the match until the discriminatory behaviour stops. Finally, if the chanting persists, referees can abandon the match. However, often match officials are not aware of the chanting.
Russia has long had a problem with racism among football supporters and campaigners fear the World Cup could be marred by such incidents.
However, the Confederations Cup in Russia last June, seen as a dress rehearsal for the World Cup, passed off largely without incident.
Experts have warned that Russian fan hooliganism could also be a threat at the world's most watched sporting event, which begins on June 14.
