The 25-year-old was visibly angered by manager Xabi Alonso's decision to pull him off in the 72nd minute for fellow countryman Rodrygo, storming off straight to the changeroom in disdain.
According to ESPN, Vinicius was due to meet with his head coach to discuss the issue on Wednesday morning following a two-day break, with the player issuing a statement on his X account.
"Today I want to apologise to all Madrid fans for my reaction to being substituted in El Clásico," stated the Brazilian.
"Just as I did in person during today's training session, I also want to apologise again to my teammates, the club, and the president.
"Sometimes my passion gets the better of me; I always want to win and help my team. My competitive nature stems from the love I feel for this club, and everything it represents.
"I promise to keep fighting every second for the good of Real Madrid, as I have done since day one."
Vini has scored five goals and provided four assists in La Liga this season but is yet to open his account in the UEFA Champions League.
The top of the table Los Blancos will take on 18th placed Valencia next at the Santiago Bernabeu on Saturday.