Russian champions also face UEFA charge over crowd disorder with a decision expected by the body on October 3.
Croatia are to face a disciplinary hearing over their Euro 2016 qualifier at home to Italy during which a swastika cross was imprinted on to the pitch, UEFA said.
UEFA, without specifically mentioning the swastika, said Croatia had been charged with “racist behaviour” and would face a hearing on July 16 at which they are expected to receive a stiff punishment.
The Croatians have repeatedly been in trouble with UEFA’s disciplinary tribunal.
Croatia fans twice caused the match away to Italy last November to be interrupted when they hurled missiles on to the pitch.
As a result, UEFA ordered Croatia to close part of the ground for the match against Norway in March at Zagreb’s Maksimir stadium.
That game was marred by further trouble as fans again threw missiles on to the pitch and Croatia were ordered to play Friday’s match in Split behind closed doors.
Croatia President Kolinda Grabar-Kitarovic called for a swift investigation and said the swastika incident had caused “immeasurable damage” to the country’s reputation.
Friday’s 1-1 draw left Croatia top of Group H with 14 points from six games, two ahead of Italy and four clear of Norway.
Bosnia have been charged with “disruption of a national anthem”, and over the throwing of objects by supporters, during their 3-1 home win over Israel in Zenica on Friday.
Northern Ireland were also charged following unruly crowd behaviour by supporters during Saturday’s 1-1 draw with Romania.