Red Star, who will serve the ban in their next home game against Vojvodina Novi Sad on Saturday, must also pay a fine of one million dinars (10,000 euros).
Champions and first division leaders Partizan were ordered to pay a fine of 400,000 dinars for the misbehaviour of their fans during last month's 2-0 win at their bitter foes.
Rival fans launched 200 flares and dozens of stun grenades during the ill-tempered derby, which was held up twice for billowing smoke to clear from the cauldron of Red Star's Marakana Stadium.
Partizan players were also unable to go the dressing-room at half-time and had to return to their dugout after Red Star fans shelled them with firecrackers following a touchline brawl between rival players and staff at the interval.
League leaders Partizan, chasing a record fifth successive league title, are seven points ahead of second-placed Red Star with one round of matches remaining before the December-February winter break.
