The Russian club were charged after apparent monkey noises were aimed at Manchester City's Yaya Toure during last week's Champions League game between the two clubs at the Arena Khimki.
The sanction will apply to CSKA's next home match in the competition, against Bayern Munich on November 27.
CSKA had vehemently denied Toure's claims that he had been racially abused during the game.
UEFA has taken a different view following a hearing of its control and disciplinary body in Switzerland, for which City submitted evidence.
UEFA believes the punishments handed out this season mark a step up in the fight against discrimination, having been criticised for fines widely considered as inadequate in previous years.
A statement read: "The fight against racism is a high priority for UEFA.
"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."
Under the regulations, a second offence of racial abuse concerning spectators could result in a full stadium closure.
Toure, who had been captaining City on the night, complained to Romanian referee referee Ovidiu Hategan when he felt he had been abused early in the second half.
There were later further apparent incidences of monkey-chanting when the Ivory Coast international had been in possession.
CSKA said they were "surprised and disappointed" by Toure's claims, which they believed were "unfounded".
But City backed their player and submitted a formal complaint to UEFA the following day, which they have since supported with witness statements.
Toure was so upset about the incident that he even raised the possibility of a player boycott of the 2018 World Cup in Russia if the issue was not tackled.
Toure said at the time: "If we aren't confident at the World Cup, coming to Russia, we don't come."
He added: "I want to see UEFA do something and take some action.
"We have to be as strong as possible otherwise they will continue like that.
"Maybe they could ban the stadium, I don't know, for a couple of years or a couple of months."
City, who won the match 2-1, are due to meet CSKA again in their next Group D fixture at the Etihad Stadium next week.
City were last involved in such an incident in February 2012 when Porto fans directed racial abuse, primarily, at Mario Balotelli.
The Portuguese club were later fined B£16,700 by UEFA.
City and CSKA are yet to issue a response to the latest verdict.