The 22-year-old Brazilian international has often been targeted by opposition fans in Spain's La Liga and was once more in a 1-0 loss at Valencia on Sunday.
The game was held up for several minutes and the referee wrote in his post-match report that shouts of "monkey" had been directed at Vinicius.
The prosecutor's office in Valencia is investigating a possible hate crime, a judicial source told AFP.
Real Madrid said earlier it had filed a complaint "in order that the facts be investigated and those responsible be held accountable".
The club said the chants, in its view, "constitute a hate crime".
Brazil formally protested to the Spanish ambassador and will lodge an official complaint with authorities in Madrid.
There is growing anger in Brazil, where the lights of the Christ the Redeemer statue in Rio de Janeiro were turned off for one hour in solidarity with the player.
"Black and imposing," Vinicius tweeted of the darkened statue, saying he was moved and thanked followers for their support.
"But I want, above all, to inspire and bring more light to our fight," he added.
Vinicius has been racially abused at several stadiums this season in Spain. On on
e occasion, an effigy of him was hung from a bridge by Atletico Madrid fans.
During the Valencia match, Vinicius stood in front of home fans behind one goal and pointed to an apparent culprit. The play was delayed for several minutes in the second half.
Referee Ricardo de Burgos Bengoetxea spoke to Mestalla stadium officials, who announced racist insults to stop before play resumed 10 minutes later.
Spain's government sports council is analysing crowd images to root out the fan or fans responsible.
The body has in similar incidents in the past proposed a one-year stadium ban and a fine of €4,000 ($4,300) for those found guilty.
On a day of recriminations and soul-searching, the head of Spain's football federation said the country had a "problem" with racism.
"As long as there is just one fan, a single undesirable, or group of undesirables who hurl insults over someone's sexual orientation, or skin colour, we have a serious problem," Luis Rubiales said.
But Real Madrid heavily criticised Rubiales, saying his refusal to ensure FIFA protocols — which suggest matches should be halted when racist abuse is heard — are upheld in Spain is exacerbating the problem.
"His inaction has resulted in the helplessness and defencelessness of our player Vinicius," said the club, which hit out at the federation for failing to "prevent the situation".
La Liga argues it has been "proactive" in previous cases of racism against Vinicius.
Vinicius was sent off in added time at the end of the game for hitting Valencia player Hugo Duro during a brawl.
Real said the match officials "made unfair decisions based on incomplete images" when Vinicius was shown a red card.
After the match, Vinicius issued a strongly worded statement saying that "today, in Brazil, Spain is known as a country of racists".
"The league that once belonged to Ronaldinho, Ronaldo, Cristiano (Ronaldo) and Messi now belongs to racists," Vinicius added.
World football and beyond have rallied around Vinicius and demanded action.
Brazilian President Luiz Inacio Lula da Silva condemned the abuse, telling a news conference at the close of the G7 summit in Hiroshima: "He was attacked. He was called a 'monkey'."
He called for the Spanish league to take "serious measures".
Real Madrid coach Carlo Ancelotti said Spanish football needed to be prepared to halt matches.
"The Spanish league has a problem, and Vinicius is not the problem. Vinicius is the victim," Ancelotti said on Sunday.
"What has happened today has happened before, but not like that, it's unacceptable," he told reporters.
FIFA reiterated that stopping matches is permitted as well as players walking off the pitch in their three-step approach when racist abuse takes place.
"Full solidarity with Vinicius," FIFA president Gianni Infantino said in a statement.