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 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.
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.
UEFA have yet to reveal the outcome of their investigation into why referee Hategan did not follow correct procedure in the event of a player complaining about racial abuse.
Officials are supposed to report such a complaint to the stadium safety officer so a public announcement can be made asking fans to desist.