A 21-year-old Red Star fan was shot with a firearm in the abdomen during their 1-0 win over OFK Belgrade and is recovering while the assailant, identified by police as a fellow Red Star supporter, is still at large.
"The ban pertains to Red Star's home matches in the Serbian first division and the national Cup, and the mitigating circumstance is that the Red Star fan club condemned the violence," FSS said.
Red Star general secretary Andrija Kleut called the ban "too harsh" and said the club would appeal.
"The measure will also not help resolve the problems we have with hooligans," Kleut said after learning the verdict.
"We knew we would be punished but the FSS should realise that there is nothing more Red Star could have done to prevent the incident," he added.
Serbian football has been rife with violence in the past 10 years. Most recently, a French fan died in a Belgrade hospital last September after he was brutally beaten up by Partizan Belgrade fans ahead of a Europa League match against Toulouse.
In September 2008, a Red Star fan was sentenced to 10 years in prison after he was convicted of attempted murder for attacking a plainclothes policeman with a burning flare during a league match in December 2007.
Red Star are two points ahead of Partizan in their two-team title race and Belgrade's bitter foes meet in a potentially explosive derby, which has a history of crowd trouble, on May 8.
Red Star play northern rivals Vojvodina Novi Sad in next month's Cup final.
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