According to a statement released by the German club on Thursday, around 500 fans riding on 10 buses turned around and did not attend the match, won 5-1 by Crvena Zvezda, after "unacceptable" treatment at the Serbian border.
The statement called the treatment "disproportionate and degrading," with "reports of physical violence" against fans. Several fans also reported being attacked in downtown Belgrade on matchday.
The club, who had fan representatives on-site to monitor and moderate the actions of security forces, have called for an investigation and is "considering filing an official claim to UEFA."
UEFA have already begun an investigation into the incident.
Stuttgart chairman Alexander Wehrle said football fans were confronted with "prejudice, harassment and the use of violence and humiliation".
"Politicians, UEFA and the clubs must take their responsibility seriously so that incidents like those in Belgrade yesterday are not met with well-intentioned communication campaigns and lip service alone."
