The Brazil international was allegedly subjected to racist chants from Real Valladolid fans in a La Liga game on Friday.
Real Madrid emerged 2-0 victors on the day thanks to a late Karim Benzema brace.
Vinicius was also subjected to racist chants from Atletico Madrid supporters back in September.
The perpetrators went unpunished as those involved could not be identified by the authorities.
In a statement on Twitter, Vinicius wrote: 'Racists keep going to stadiums and watching the biggest club in the world up close and La Liga goes on doing nothing.
'I will follow with my head held high and celebrating my victories and Madrid. In the end it's my fault.'
A La Liga spokesperson said "hate speech has no place" in the league.
They added: "We are investigating last night's match and, as always in these cases, will work with the clubs and appropriate authorities to identify and prosecute anyone guilty of hate speech.
"La Liga has detected videos uploaded to social networks of racist insults from a person, not from groups, and they will be charged as in previous cases.
Vinicius has scored six goals and provided three assists in 15 La Liga games this season.
