Real Madrid said they would punish midfielders Federico Valverde and Aurelien Tchouameni after a clash on Thursday at the club's training ground which left the former needing hospital treatment.
"Following the incidents that occurred this morning during the first team's training session, (the club) has decided to open disciplinary proceedings against our players Federico Valverde and Aurelien Tchouameni," said Los Blancos in a statement.
Uruguay international Valverde was accompanied to the hospital facility near the club's Valdebebas training complex by Madrid coach Alvaro Arbeloa, according to Spanish reports, which said he needed stitches to treat a facial wound.
Madrid said Valverde had suffered a head injury but was in "good condition" and needed to rest for up to a fortnight.
The 27-year-old will therefore miss Sunday's Clasico clash with rivals Barcelona in LaLiga, where the Catalans can claim the Spanish title.
According to reports the two players rowed on Wednesday in training and their argument continued on Thursday during and after the session.
Spanish newspaper Marca, who first reported the story, said Valverde's cut was caused unintentionally and not directly by a punch from France midfielder Tchouameni.
Real Madrid and the agents of the two players did not comment when contacted about the incident by AFP.
Spanish media reported Valverde refused to shake Tchouameni's hand and later fouled him in Thursday's training session, with the pair scrapping afterwards in the dressing room when the injury occurred.
Tensions are running high at Real Madrid with the club on the verge of a second consecutive season without a major trophy.
Los Blancos trail Barca by 11 points at the top of LaLiga, with Hansi Flick's side able to clinch back-to-back league titles this weekend if they do not lose.