Real gained at Atletico Madrid on Sunday and a few opposing fans allegedly sang racist songs when coming into the bottom.
It comes after Vinicius, 22, said “the happiness of a black Brazilian in Europe” was behind current criticism.
“We denounce all incidents inside and outside stadiums,” said a La Liga spokesperson.
“We work with clubs to keep our football friendly and enjoyable.”
The spokesperson added: “Hate speech has no place in La Liga and we always work with the clubs and the authorities to identify and bring to justice any such case.”
Vinicius’ celebration after scoring, through which he dances, have drawn feedback from pundits in Spain lately.
Agent Pedro Bravo said throughout a Spanish tv dialogue on Vinicius that “in Spain, you have to respect rivals and stop playing the monkey”, main to accusations of racism. He has since apologised.
Brazil worldwide Vinicius, who has scored 5 goals in eight games for the European champions up to now this season, listed other stars who danced of their celebrations in a statement on Friday.
“Weeks ago, some people started to criticise my dancing. But the dancing is not mine alone,” he said.
“They belong to Ronaldinho, Neymar, [Lucas] Paqueta, [Antoine] Griezmann, Joao Felix, Matheus Cunha… Brazilian funk singers and samba dancers, Latin reggaeton singers, Black Americans. They are dances to celebrate the cultural diversity of the world.