The Russian champions are also forbidden to sell away tickets for their trip to face Manchester City in UEFA Champions League Group E later this month.
The punishments relate to incidents during CSKA's opening 5-1 defeat at Roma in this season's competition, when play was halted due to crowd disturbances, for which the club has also been fined €200,000.
In a statement, UEFA confirmed CSKA had fallen foul of Article 14 of its disciplinary regulations: "racist behaviour of supporters"; and two sections of Article 16: "crowd disturbance and setting/off throwing of fireworks and missiles".
The statement added: "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 field 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."
It is the third time in the past year that CSKA have been punished due to racist behaviour by the club's supporters.
Manchester City midfielder Yaya Toure was subjected to monkey noises as the Premier League champions secured a 2-1 win in Russia last October. A section of CSKA's ground was closed for the next home game against Bayern Munich
In December, UEFA charged CSKA for supporters displaying far-right symbols during the 2-1 away loss at Viktoria Plzen.
For the latter offence, CSKA was forced to play this week's 1-0 defeat to Bayern in a closed stadium.
Elsewhere, Ukrainian club Dnipro must play its forthcoming Europa League home game against Azerbaijani champions Qarabag with a section of its stadium closed as part of a UEFA punishment for displaying a racist banner, setting off fireworks and the use of a laser pointer in the crowd.
Dnipro has also been fined €24,000 and ordered to display a banner with the wording "No to Racism" following incidents at their 1-0 loss to Inter last month.
Disciplinary proceedings have also been opened following Thursday night's Europa League game between Feyenoord and Standard Liege.
The Dutch hosts, who won 2-1, are being investigated for breaches relating to the setting off of fireworks and insufficient crowd organisation. The visiting Standard supporters could bring punishments on their club duel to crowd disturbances and the setting off of fireworks.
