The Russian side were charged after their supporters were accused of racist chanting aimed at Manchester City midfielder Yaya Toure on 23 October.
The Ivory Coast international complained during and after the match about the racist abuse but CSKA have disputed the accuracy of his claims.
However, UEFA have decided to sanction the club following a hearing of its control and disciplinary body in Switzerland, and section D of the stadium - where the offence occurred - will be closed against Bayern.
The governing body have previously been criticised for only issuing fines in such cases and have stressed that the partial closure of grounds represents a step forward in the battle against discrimination.
Full closure the next step
"The fight against racism is a high priority for UEFA," said a statement.
"The European governing body has a zero-tolerance policy towards racism and discrimination on the pitch and in the stands.
"All forms of racist behaviour are considered serious offences against the disciplinary regulations and are punished with the most severe sanctions.
"Following the entry into force of the new disciplinary regulations on 1 June, the fight against racist conduct has been stepped up a level, resulting in more severe sanctions to deter any such behaviour."
If CSKA Moscow are found guilty of a second offence of racial abuse by their supporters they could be punished with a full stadium closure.
Inclusion campaigners Kick It Out released a statement saying: "(We) acknowledge the swift, decisive and proportionate sanction delivered by UEFA in accordance with its regulations.
"Yaya had the courage to raise this as an issue and we need to gauge if he thinks this is a satisfactory step.
"The other aspect of this is the viewpoint within CSKA Moscow. If the club deny there is an issue, this will prevent meaningful, lasting progress from being made."
Toure complained to referee Ovidiu Hategan when he felt he was abused early in the second half of last week's match but there seemed to be further incidents of monkey chanting when he was in possession later on in the contest.
Formal complaint made
CSKA said Toure's claims were "unfounded" but City made a formal complaint to UEFA the following day, which they subsequently backed up with witness statements.
And a distressed Toure has raised the possibility of players boycotting the 2018 World Cup in Russia if the racism problem is not addressed.
In a separate announcement, UEFA has relieved its venue director from that evening of his duties for failing to make a public announcement calling for the abuse to stop.
Referee Hategan has been cleared of any blame as to why that did not occur, following an internal UEFA investigation.