LaLiga made a complaint about the fans to the police and said they had provided video and audio recordings they had gathered.
The commission also held an extraordinary meeting on Monday to discuss another incident involving the 22-year-old Brazilian.
A dummy dressed in a Vinicius shirt was strung up near Real Madrid's training ground before last week's Copa del Rey quarterfinal against local rivals Atletico with a message reading "Madrid hates Real."
The CSD said police had begun an investigation to identify those behind the "despicable acts" using traffic cameras and images published on social media.
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