CSKA's punishment applies to Section D at Arena Khimki when defending champion Bayern visits on Nov. 27.
UEFA can choose to appeal to impose a tougher sanction.
"All forms of racist behavior are considered serious offences against the disciplinary regulations and are punished with the most severe sanctions," UEFA said in a statement.
The club and senior Russian football officials have denied any racial abuse happened, and even suggested a British conspiracy against the 2018 World Cup host.
CSKA is the ninth club to be punished by UEFA this season for racist behavior by fans at Champions League or Europa League matches after tougher penalties were agreed upon in May.
Dinamo Zagreb and Legia Warsaw have been convicted of repeated offenses and ordered to play one match in an empty stadium. Six clubs had partial closures imposed for first offenses: Lazio, APOEL Nicosia, Honved, Lech Poznan, Piast Gliwice and Rijeka.
UEFA did not fine CSKA, which has already earned prize money of 8.6 million euros ($11.8 million) just for qualifying for the group stage.
UEFA opened a disciplinary case based on a formal complaint by City, and reports from Hategan and match delegate Tormod Larsen of Norway.
However, UEFA President Michel Platini requested an internal inquiry involving the referee to examine why guidelines were not followed to respond to discrimination incidents during matches.
"The referee immediately asked the fourth official to request an announcement to be made to the public," UEFA said. "The venue director (the UEFA officer in charge of football operations), who had not heard the chanting himself, did not activate the procedure."
"As the chanting had ceased, the referee decided to resume the game with the free kick," UEFA said. "The UEFA venue director at the Arena Khimki has been relieved of his duties."