That provoked a response from LaLiga President Javier Tebas who wrote on Twitter that it is doing enough and that Vinicius should inform himself "before you criticise and slander LaLiga".
"The first thing is to recognise that we have a problem in our country," Rubiales said at a press conference in Madrid on Monday. It is "a serious problem that also stains an entire team, an entire fan base, an entire club, an entire country."
The Brazilian government on Monday summoned the Spanish ambassador to explain the incident. The Spanish government's response was muted, with condemnation issued by only junior ministers, as the country gears up for regional elections at the weekend.
The match at the Mestalla stadium in Valencia was stopped for 10 minutes after Vinicius pointed out fans who were allegedly hurling racist comments at him.
Videos posted on social media and verified by Reuters showed hundreds of Valencia fans singing "Vinicius is a monkey" as the Real Madrid bus arrived at the stadium before the match.
"I am sorry for those Spaniards who disagree but today, in Brazil, Spain is known as a country of racists," Vinicius Jr wrote on Twitter.
Rubiales criticised Tebas's comments, describing them as "irresponsible behaviour."
"Probably Vinicius is more right than we think and we all need to do more about racism," Rubiales said.
Real Madrid said on Monday they have lodged a hate crime complaint following the incident. It is the 10th episode of alleged racism against Vinicius that has been reported to prosecutors this season, according to LaLiga.
Valencia said in a statement they have identified one fan and are working with police to confirm the identity of others. They said they will apply a punishment that could include lifetime stadium bans for those involved.
Spanish police are also investigating a possible hate crime against Vinicius Jr after a mannequin wearing his number 20 shirt was hung from a bridge outside Real Madrid's training ground in January ahead of the club's derby match with Atletico Madrid.
Prosecutors dropped a complaint filed for racist chants aimed at the player in September during another game against Atletico Madrid.
The prosecutor archived the case because the chants of "monkey" were only said a couple of times and "only lasted a few seconds," highlighting how Spain's penal code makes it difficult to prosecute racist incidents at football games.
"LaLiga uses these legal cases to wash its hands, even though it actually has the power to make decisions and impose sanctions by itself," said Moha Gerehou, a Spanish journalist and anti-racism activist.
"LaLiga should be able to close stadiums and force a number of matches to be played behind closed doors in these cases, as that puts the pressure on the clubs and the fans themselves."
Spanish prosecutors officially investigated just three cases of racist acts during the 2021-22 season, according to the Interior Ministry. Under current rules, people found guilty of racist behaviour can be fined up to 4,000 euros ($4,403) and banned from stadiums for a year.
There is growing momentum for Spain to do more to tackle the problem. Brazilian President Luiz Inacio Lula da Silva called on FIFA and LaLiga to "take real action".
Seven-times Formula One world champion Lewis Hamilton sent Vinicius a virtual fist bump on Instagram, adding: "Standing with you @vinjr."
FIFA President Gianni Infantino called for LaLiga to enforce a rule that penalises clubs with points deductions if racist chants persist and said racists should be banned for life from stadiums worldwide.