Gareth Bale's car was punched and kicked by angry fans as he left the Valdebebas training ground, having returned from Barcelona following Real's 2-1 Clasico loss.
In a statement, the La Liga giants said the individuals had been identified "for these aggressive and violent actions against several of our players".
The club's discipline commission opened action and provisionally suspended the member's rights and access to The Santiago Bernabeu and any of Real's facilities.
"Real Madrid has notified Spain's National Anti-Violence Commission of the incidents that took place, as well as the identities of the individuals responsible, requesting that it apply those sanctions that it considers appropriate," part of the statement read.
"Furthermore, Real Madrid will take any applicable legal action against the individuals responsible for these incidents."
Jese Rodriguez was abused as he left the complex, while Sergio Ramos confronted the fans as he departed.
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