The punishment, handed down by the BFU disciplinary commission, will come in to effect for Botev's highly anticipated home game against leaders Litex Lovech on Saturday.
The Plovdiv-based side were also fined 4,000 levs (1,750 pounds) for the incidents. Levski were fined 2,000 levs for not being able to control the away fans in the game they won 1-0.
Two-times Bulgarian champions Botev are fifth in the standings on 25 points from 15 matches, nine points behind Litex. Levski are sixth also on 25 points.
Earlier this week, Lokomotiv Plovdiv were ordered to play their next home match behind closed doors after crowd violence marred their 1-0 win over CSKA Sofia.
Violence inside and outside stadiums has plagued Bulgarian football in recent seasons, endangering the safety of players and fans.
(Reporting by Angel Krasimirov; Editing by John O'Brien)
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