"A 20-year old fan has sustained an abdominal wound from a firearm, he is undergoing surgery and is in critical condition," Anlave clinic director Slobodan Ivanovic was quoted as saying by Belgrade's B92 television.
"He was rescuscitated on the scene after a fight broke out midway through the second half of the match and two other individuals sustained minor injuries," Ivanovic added.
"The fan was rushed to hospital by our ambulance from the stadium immediately after the incident, which took place in the north tier occupied by Red Star supporters."
Serbian football has been rife with violence in the past 10 years and fights between rival fans have often resulted in fatalities.
Most recently, a French fan died in a Belgrade hospital last September after he was brutally beaten up by Partizan Belgrade fans ahead of the team's Europa League match with French side Toulouse.
Red Star beat city rivals OFK 1-0 on Wednesday with a late goal from striker Dejan Lekic to reach their first Serbian Cup final since 2007, with holders Partizan playing Vojvodina Novi Sad in the other semi-final on Thursday.
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