CSKA was ordered to play its next three UEFA competition matches in an empty stadium by UEFA's disciplinary panel on Friday.
The Russian champion hosts Manchester City on Oct. 21 and Roma on Nov. 25 at Arena Khimki. The third closure will apply at a future match.
UEFA also barred CSKA from selling tickets to its fans for away matches at Man City and Bayern Munich.
The punishments are for incidents during CSKA's 5-1 loss at Roma last month. Fans displayed far-right banners and fought police in the Olympic Stadium.
CSKA lost 1-0 to Bayern in an empty stadium this week because of "racist behaviour" incidents last season.
UEFA has imposed an escalating series of sanctions against CSKA after giving itself tougher judicial powers last year.
"The fight against racist conduct has been stepped up a level — resulting in stricter penalties to deter any such behaviour," UEFA said in a statement.
UEFA also fined CSKA 200,000 euros ($252,000), including additional offences for fans lighting flares and throwing missiles.
The club can appeal.
CSKA noted the disciplinary decision in a statement on its website without further comment.
The club's president, Evgeni Giner, sits on a key UEFA policy-making panel. He is one of four European club representatives on the strategy council chaired by UEFA President Michel Platini.
CSKA has been charged with racist behaviour by its fans at three Champions League matches in less than a year, including a home game against Man City last season.
Then, visiting captain Yaya Toure, who is black, directed the match referee to home fans making monkey noises.
CSKA and senior Russian football officials later denied the abuse happened.
UEFA then charged CSKA in December for fans displaying far-right symbols at a match at Viktoria Plzen. The stadium closure for that offence was applied when Bayern visited on Tuesday.
In a separate case Friday, UEFA punished Ukrainian club Dnipro Dnipropetrovsk for incidents involving fans at a Europa League match against Inter Milan last month.
UEFA had charged Dnipro with offences of "racist behaviour" and displaying an offensive banner at the Olympic Stadium, Kyiv. Dnipro plays in the capital after UEFA judged its home city in eastern Ukraine unsafe during the current conflict with pro-Russia separatists.
Dnipro must close a section of the stadium when it hosts Qarabag of Azerbaijan on Oct. 23.
The club must cover that section with a "No to Racism" banner and the UEFA logo, the sanction stated.
UEFA said it also fined Dnipro 24,000 euros ($30,000).