AFP photographers at Partizan's Stadion Partizana said the fight broke out in a section of the stadium housing home fans and lasted around 10 minutes.
One photographer said the fight was between rival groups of Partizan fans.
Police were forced to intervene to end the scuffles while several fans, some with bloodied faces, were evacuated from the stadium.
The match finished 1-1 after Red Star's Richmond Boakye equalised six minutes from time after a Seydouba Soumah penalty had given Partizan a second-half lead.
Since the break up of the former Yugoslavia, the Belgrade derby has often been beset by hooligan problems.
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