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Some home fans hurled abuse at the Brazilian winger during Madrid's 2-0 win at Valladolid on December 30, prompting La Liga to file a complaint to the local courts.
The CSD said in a statement that its Commission against Violence, Racism and Xenophobia in sport has "initiated proceedings for the proposed punishment of more than 10 supporters" over the incidents.
Police are collecting data before recommending punishments, which could include fines of 4,000 euros (around $4,300) and a one-year ban from sports stadiums for any person identified, the statement added.
La Liga 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 quarter-final 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.
Earlier this season, Spanish prosecutors opened an investigation into racist abuse against Vinicius by Atletico Madrid fans based on footage of chants calling him a monkey before last September's Madrid derby.
The prosecutors closed the probe saying it was impossible to charge a specific individual despite the "unpleasant, inappropriate and disrespectful" nature of the chanting. - AFP
