Mallorca fans were filmed racially abusing the forward during Sunday's win against the LaLiga holders, with the video published by streaming company DAZN on social media.
"LaLiga has forwarded all the information gathered, together with its complaint, both to the Court of Instruction in Palma de Mallorca, and to RCD Mallorca so that it can participate in the case," said the statement.
It is the sixth complaint LaLiga has filed for racist chanting or insults against Vinicius.
Earlier on Tuesday, Real coach Carlo Ancelotti (63) said the abuse that has been directed at Vinicius is a problem for the whole of Spanish football.
"It seems that the problem is Vinicius, and it is not like that. It is a problem of Spanish football and it must be solved," Ancelotti told a news conference in Rabat ahead of the Club World Cup semi-final against Egypt's Al Ahly.
"The question I ask is this: Is it Vinicius or his teammates? What do his teammates have to defend Vinicius from? Vinicius is the victim of something that I don't understand."
Spanish police are also investigating a possible hate crime against the Brazilian after a mannequin wearing his number 20 shirt was hung from a bridge in front of the club's training ground ahead of the Madrid derby two weeks ago.
