FIFA have charged the Russian Football Union with fan racism following incidents during the national team's friendly with France in March.
French duo Paul Pogba and Ousmane Dembele were among those said to be targeted by monkey noises during the game against the World Cup hosts in St Petersburg.
"We can confirm that disciplinary proceedings have been opened against the Russian Football Union for this incident. We have no further comment at this stage," a FIFA spokesperson said.
UEFA opened disciplinary proceedings against Zenit - whose Krestovsky Stadium hosted the international fixture - in March after racist chants were allegedly heard during a Europa League last-16 tie against RB Leipzig.
The venue will stage a World Cup semi-final on July 10, as well as group matches including Russia v Egypt, Brazil v Costa Rica and Nigeria v Argentina.
