The chants of fans towards Real Madrid's Vinicius Junior were unacceptable and have been condemned by Atleti Madrid.
They will co-operation with the authorities.
"These chants make people angry and revulsion," the statement said.
"We won't allow anyone to hide behind our colors to say bad things about us or our culture."
La Liga said it will work with authorities to identify and bring to justice the culprits of hate speech.
Vinicius' goal celebration, in which he dances by a corner flag, was criticized by some commentators in Spain.
The Brazil forward said that the happiness of a black Brazilian in Europe was the reason for recent criticism.
The authorities were asked to identify the fans who took part in the chanting so that they could be expelled from the club.
The club has always been known for being an open and inclusive space for fans of different nationalities, cultures, races, and social classes, and a few cannot tarnish the image of thousands and thousands of Atleti fans who support their team with passion and respect for their opponents
We have zero tolerance for racism and will not stop until it is eliminated.
The pain felt by the red and white family is huge. We can't allow anyone to link our fans with this behavior because a minority doesn't represent us.
In Spain, you have to respect rivals and stop playing the monkey, according to an agent on Vinicius. He hassince apologized.
Brazil international Vinicius, who has scored five goals in eight games for the European champions so far this season, listed other stars who danced in their celebrations in a statement on Friday.
Vinicius was supported by several Brazilian football stars on social media, including Pele and Neymar, while Real Madrid also released a statement condemning the pundit's comments on Friday.
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