The Brazilian, who joined Partizan last year, played through monkey chants and other abuse, including a racist banner in the stands where Rad fans were standing.
The banner was removed after intervention from the referee.
Huge scuffles broke out between the players after the match on Sunday, which Partizan won 1-0, after Luiz showed the middle finger to the Rad supporters.
Wiping away tears, Luiz said he "faced racist abuse during the entire match."
Rad Belgrade have now been ordered not to play first division matches in their home stadium until Serbian football authorities rule over the racial insults.
"Due to the misbehaviour of their fans who racially insulted a player, Rad's stadium has been suspended until the Serbian Football Association (FSS) passes a verdict," league commissioner Vladimir Bulatovic said.
"The suspension means no first division games will be played at the venue until a final decision is made and disciplinary proceedings have been opened against all parties involved in the incident."
Rad fans abused Luiz throughout the ill-tempered match and a full-scale player brawl broke out when he retaliated with an obscene gesture after the final whistle.
Staff from both teams jumped in to quell the fighting after Rad players confronted Luiz, who left the ground in tears and issued a statement expressing his affection for Serbia while condemning the offenders.
"My family and I feel at home in Serbia and this is why I could not stop the tears after the game," he said.
"I took 90 minutes of racist abuse and other insults from the terraces and thereafter I found myself in a cauldron of emotionless individuals who charged at me when they should have protected me.
"I want to forget this, refocus on football and urge everyone to say 'No' to racism."
Partizan won the match 1-0 at the Rad stadium thanks to an Uros Djurdjevic goal which kept them second in the 16-team league, six points behind champions and leaders Red Star Belgrade.
