The campaign launched on social media under the hashtag #MetropolitanoConMascarilla ('Metropolitano with a mask') aims to encourage Atletico fans to don masks at the Metropolitano Stadium on Sunday in order to racially abuse the Brazilian winger without revealing their identities.
Multiple arrests have been made in Spain since last year for racist abuse directed at Vinicius.
"La Liga wishes to announce that it will proceed to formally report and request the immediate arrest of the instigators behind a hate campaign seeking to promote racist and derogatory acts," La Liga said in a statement on Saturday.
"The campaign constitutes the crime of incitement to hatred, as clearly defined in the Penal Code. La Liga vigorously condemns these actions that - directly or indirectly - encourage, promote and incite hatred against an individual, in this case, the player Vinicius Jr, because of his race.
"These acts not only harm the image of the sport and our country but also pose a direct threat to the integrity and well-being of all fans."
Last year, four Atletico fans were charged for hanging an effigy of Vinicius from a bridge in Madrid and three Valencia fans were sentenced to eight months in prison in June for hate crimes against the Brazilian.
Real Madrid also filed a complaint in March with the state prosecutor's office after a social media video showed alleged racist chanting by Atletico fans ahead of their team's Champions League match against Inter Milan.
Atletico were also ordered to partially close their south stand for two matches by the Spanish Football Federation (RFEF) after Athletic Bilbao player Nico Williams suffered racist abuse in April.
