Vinicius was recently criticised by Spanish football agent Pedro Bravo, who accused the Brazilian of being disrespectful when he danced after scoring against Real Mallorca last weekend.
His comments sparked outrage as Bravo stated that Vinicius should "stop playing the monkey" during his outburst, leading to racist accusations.
Hundreds of Atletico supporters could be heard singing, "Vinicius, you are a monkey, you are monkey" in a video published on social media by radio station Cope in the build-up to the Madrid derby, which Real won 2-1.
Local media also reported that monkey noises and chants of "Vinicius, die" were heard throughout the game.
"We denounce all incidents inside and outside stadiums," a LaLiga spokesperson told the BBC. "We work with clubs to keep our football friendly and enjoyable.
"Hate speech has no place in LaLiga and we always work with the clubs and the authorities to identify and bring to justice any such case."
The clubs have not commented on the incidents.
