A 44-year-old man who suffered a heart attack an 11-year-old boy with head injuries were rushed to Belgrade's Emergency Centre while three of the arrested faced criminal charges.
"Eight people were arrested before and during the match and 32 afterwards," Belgrade police chief Slobodan Vukolic told the state Tanjug news agency.
"Three of the arrested face criminal charges while police will keep working to identify other offenders who set fire to stadium seats," he said.
The derby match, which ended in a 2-1 win for champions Partizan, was held up for several minutes in the second half as firemen and riot police moved on to the athletics track around the pitch to put out fires.
The Belgrade derby has a history of crowd trouble. Fierce rivalry between the fans has resulted in several deaths in and outside stadiums.
In 1999, a Red Star fan was killed by a burning flare launched by Partizan fans from their end of the stadium.
In September, a fan of French first division side Toulouse died in Belgrade 12 days after a group of Partizan fans beat him up before the two teams played a Europa League match.
In Saturday's game, Partizan outplayed league leaders Red Star despite being reduced to 10 men for most of the second half.
They cut the deficit in the league table to one point after Brazilian striker Cleo, who became the first player in 20 years to move between the two Belgrade sides during the close season, scored a spectacular winner.
Cleo curled in a superb shot from 18 metres after a Srdjan Knezevic own goal had cancelled out Lamine Diarra's early opener for Partizan.
Red Star have 34 points from 13 games, Partizan have 33 and third-placed Vojvodina Novi Sad, who visit Rad Belgrade on Sunday, have 24.
