The 1-1 draw was suspended for 20 minutes as fans threw objects onto the pitch and targeted visiting goalkeeper Thibaut Courtois.
Atletico stated afterwards: "Atlético de Madrid wishes to express its rejection of the throwing of objects from part of the south end of the stands in the 68th minute of the match against Real Madrid. From the moment the objects were thrown, the club's security department has been working with the police to locate those involved, one of whom has already been identified.
"The club will apply the internal regime provided for very serious cases to those involved in this incident.
"These attitudes have no place in football and tarnish the image of a stadium that has experienced a spectacular atmosphere with more than 70,000 spectators in its stands and the vast majority of whom have shown exemplary behaviour."