The Russian club's supporters will also be prevented from attending their remaining two Champions League away group games this season against Manchester City and Bayern Munich, European soccer's governing body added in a statement.
CSKA's fans were found guilty of a series of offenses including "racist behaviour of supporters, crowd disturbance, setting off/throwing of fireworks and missiles" during their Group E fixture against AS Roma in Italy on Sept. 17.
"The European governing body has a zero-tolerance policy towards racism and discrimination on the field and in the stands," UEFA said.
"All forms of racist behaviour are considered serious offences against the disciplinary regulations and are punished with the most severe sanctions."
CSKA fans fought with Roma supporters before the match and clashed with police afterwards in incidents which left 13 stewards and four officers injured. Roma won the game 5-1.
CSKA have already played their first Champions League home match against Bayern on Sept. 30 behind closed doors as punishment for their fans' racist behaviour last season.
They were found guilty of racist chanting during matches against Manchester City and Viktoria Plzen.
"Of course we are really upset with the decision," CSKA's press spokesman Sergei Aksenov said.
"Thanks to a few people, the festival of football that is the Champions League, has been turned into a series of ghost matches, as these matches without supporters are already being called. It's all very sad and upsetting."
CSKA have not ruled out appealing the decision.
"We need to wait to hear the reasoning for their decision," Aksenov added.
"Only then will it become clear if the punishment is fair and whether we may try to launch an appeal."
Russia's Minister for Sport Vitaly Mutko told R-Sport: "It's a harsh punishment, very harsh, but it could have been worse. Some clubs have been excluded from the Champions League."
(Reporting By Dmitriy Rogovitskiy; editing by Toby Davis)
