Red Star quintet Marko Gobeljic, Njegos Petrovic, Dusan Jovancic, Marko Konatar and Branko Jovicic contracted COVID-19.
Gobeljic, Petrovic, Jovancic and Konatar had symptoms prior to Saturday's season finale and did not attend the match as a precaution.
It comes after Dejan Stankovic's Red Star celebrated a third successive SuperLiga title in front of fans in Belgrade on Saturday – defeating Proleter Novi Sad 2-1.
Red Star also played in front of a near 25,000 capacity crowd for the Serbian Cup semi-final against bitter rivals and neighbors Partizan, who won 1-0 on June 10, following the easing of coronavirus restrictions in the country.
"The aforementioned players are feeling well, and are in strict isolation as well as constant contact with the club's medical team," Red Star said in a statement on Monday.
"The condition of the players is being carefully monitored and a new test will be performed before the start of the preparations for next season."
Red Star added: "It is important to point out that all other players, management and staff who were in direct contact with the first team have received a negative result. Red Star is taking all necessary protection measures and we will continue to do so."