Monkey chants were aimed at black French players, including Paul Pogba, during France's 3-1 friendly win over Russia in St. Petersburg last month.
After collecting evidence of the abuse, FIFA says "disciplinary proceedings have been opened against the Russian Football Union (RFU) for this incident".
Russia was previously charged with racist behaviour by its fans at the last two European Championships. On both occasions, the RFU paid a fine.
It's the third racism case this season at St. Petersburg Stadium, which will host a World Cup semi-final match. Zenit St. Petersburg has twice faced UEFA charges for racism by its fans in Europa League games.
Zenit fans flew a banner praising convicted war criminal Ratko Mladic when playing a Macedonian club in November and are accused of using a racially charged term to mock an injured black player in a game against Leipzig. The second case is due to be heard by UEFA on May 31, two weeks before the World Cup begins.
(FRANCE 24 with AP)