Valencia are taking action after Vinicius was a victim of racism at Estadio de Mestalla, and have started an official investigation into the incident, according to a club statement.
The club also stated that they "publicly condemn insults and attacks of all kinds in football" but stressed that Sunday's event was an "isolated episode".
Referee Ricardo De Burgos halted play in the 73rd minute of the La Liga clash between Valencia and Real Madrid after Vinicius highlighted fans who he claimed had racially abused him.
After lengthy discussions with both Vinicius and Real Madrid manager Carlo Ancelotti, the game continued and finished.
Following the contest, Ancelotti emphasised that La Liga had a "racism problem" and demanded that the league take action against the attacks on his star winger.
The coach also argued that the game had to be stopped and said he considered taking the Brazilian off the field amid the insults.
Vinicius was eventually sent off when he slapped Valencia attacker Hugo Duro in the dying minutes of the game, which finished in a 1-0 win for Valencia.
There have already been eight separate complaints filed over abuse of Vinicius this season and the player took to Twitter to voice his anger, saying that racism has become "normal" in La Liga.
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