• Following the match, in which the 22-year-old Brazil international was later sent off for violent conduct, he said "La Liga belongs to racists".
• Vinicius has been the target of racist abuse multiple times this season.
The latest incident of racist abuse towards Real Madrid forward Vinicius Jr has been reported to the Spanish prosecutor's office as a hate crime, the club says.
Real's La Liga match at Valencia on Sunday was paused in the second half as an incensed Vinicius reported opposition fans to the referee.
Following the match, in which the 22-year-old Brazil international was later sent off for violent conduct, he said "La Liga belongs to racists".
Real Madrid issued a statement on Monday stating that it "considers that such attacks also constitute a hate crime".
Spanish prosecutors will now decide whether to pursue a criminal investigation.
"Real Madrid shows its strongest revulsion and condemns the events that took place yesterday against our player Vinicius Junior," the club said.
"These facts constitute a direct attack on the coexistence model of our social and democratic state of law."
Vinicius has been the target of racist abuse multiple times this season.
La Liga said in a statement it would investigate and take "appropriate legal action" if a hate crime was identified, calling on people to submit any relevant footage.
Valencia said police had "identified a fan who made racist gestures" and that the "club are also working along with the police to confirm the identity of any other potential offenders".
The club added: "Valencia CF have proceeded to open a disciplinary case, will apply the maximum level of severity, including a lifetime stadium ban against the fans involved, and is working closely together with the authorities."
Vinicius and Tebas Twitter row
Writing on social media after the match, Vinicius said: "The championship that once belonged to Ronaldinho, Ronaldo, Cristiano and Messi today belongs to racists."
He then exchanged messages with La Liga president Javier Tebas.
Writing on Twitter, Tebas said Vinicius twice did not turn up for a meeting to discuss what it "can do in cases of racism".
"Before you criticise and slander La Liga, you need to inform yourself properly," Tebas said.
Vinicius criticised the post for targeting him instead of the "racists", saying he wanted La Liga to take "actions and punishments".
Tebas then replied: "Neither Spain nor La Liga are racist, it is very unfair to say that.
"We have reported nine instances of racist insults this season (eight have been against Vinicius). We always identify the thugs responsible and take the complaints all the way to the relevant bodies who have power to punish them. No matter how few they are, our efforts are relentless."
He added: "We cannot allow the reputation of a competition which is above all a symbol of unity between communities, where over 200 black players from 42 clubs are welcomed with respect and love from fans every week, to be tarnished.
"Cases of racism are an extremely rare occurrence (nine reports) which we are committed to eliminating altogether."