The two adults and a minor are accused of having "made xenophobic statements that harmed the dignity and moral integrity of the two footballers" during the match which Barcelona won 4-0 in Madrid, police said.
The trio were identified using mobile phone and television footage.
Videos emerged on social media after the game of racial abuse aimed at the Barcelona players, with 17-year-old Spain star Yamal targeted during a goal celebration after becoming the youngest Clasico scorer.
Spanish football is struggling to combat racism in stadiums across the country.
Real Madrid striker Vinicius Junior has become a figurehead in the fight against racism and has been targeted on numerous occasions since arriving in Spain in 2018.
The Brazilian winger earned worldwide support in May 2023 when he squared off with Valencia supporters after suffering abuse at their Mestalla stadium.
In June three Valencia supporters were sentenced to eight months in prison as a result.
In January 2023, an effigy in a Vinicius shirt was found hanging from a bridge near the club's training ground alongside a banner saying: "Madrid hates Real."
