The 125th "eternal derby", as games between the two most popular Bulgarian clubs are called, was briefly interrupted early in the second half as firemen and riot police moved on to the athletics track around the pitch to put out fires.
"The police have arrested 19 fans before the match for grave offences against public order," said a police spokesperson. He later said five more fans were arrested after the game.
Saturday's match was a dull affair that finished goalless.
The game has a history of crowd trouble with Bulgarian police unveiling strict security measures ahead of the game.
About 1,400 policemen were on duty for the match played less than a week after CSKA's game at Lokomotiv Mezdra was abandoned midway through the second half due to crowd trouble.
Levski and CSKA's 0-0 draw came on a day when none of the chasing pack closed the gap on league leaders Litex Lovech.
Litex are top with 48 points from 21 matches ahead of Lokomotiv Sofia with 41 and a game in hand. CSKA are third with 40 points followed by Levski on 36.
CSKA squandered several chances, with Romanian striker Daniel Panku and French midfielder Elliot Grandin failing to score after the interval, while Levski did not create any.
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