The 31-times Bulgarian champions were also fined 6,000 levs ($4,240) by the Bulgarian Football Union's disciplinary commission on Tuesday.
Police forced 3,500 CSKA fans out of Levski's Georgi Asparuhov stadium at halftime after they broke the safety fences and pelted police with fireworks and other objects during the first half.
The ugly scenes continued outside the stadium in the Bulgarian capital's district of Poduene with fighting and buses, cars and shops damaged.
Police, who denied using heavy-handed tactics, arrested 23 fans on Saturday but said the number will increase as offenders are identified from video footage.
The BFU fined Levski 3,000 levs for poor organisation and for fans throwing objects on the pitch.
CSKA won the "eternal derby" 3-1.
BFU president Borislav Mihaylov met with Sports Minister Svilen Neykov earlier on Tuesday to discuss ways of combating hooliganism.
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