Real Madrid have opened disciplinary proceedings against Federico Valverde and Aurelien Tchouameni after Valverde was taken to hospital with a head injury following a fight between the pair.
The team-mates were involved in a physical confrontation at the end of training on Wednesday, with tempers understood to have flared again in training on Thursday.
Valverde was taken to hospital with what Madrid said was a "cranioencephalic trauma" but he was subsequently discharged and returned to the club's Valdebebas training ground.
The club said he was recovering at home and would be ruled out for up to two weeks.
Valverde later admitted in a lengthy statement that the pair had had a "disagreement" but denied any "fistfight", claiming he "accidentally hit a table, causing myself a small cut on my forehead that required a routine visit to the hospital."
Real Madrid's players had earlier held a crisis meeting, with the club later confirming an investigation - led by president Florentino Perez - was under way.
A statement read: "Real Madrid CF announces that, following the events that took place this morning in the first team training session, it has decided to open disciplinary proceedings against our players Federico Valverde and Aurélien Tchouameni.
"The club will announce the resolutions of both cases in due course, once the corresponding internal procedures have been completed."
The incidents have taken place in the build-up to the Clasico in Barcelona on Sunday, with Barcelona 11 points clear of Real Madrid at the top of LaLiga and needing only one point to clinch the title.
The news came at the end of a tumultuous day after fan unrest with forward Kylian Mbappe spiralled.
Mbappe is on track to feature on Sunday following a hamstring injury but a petition to see the French forward sold reached 30 million signatures on Thursday.
"Yesterday I had an incident with a teammate as a result of a play during training, where the fatigue of competition and frustration make everything seem bigger than it is.
"In a normal locker room, these things can happen and are resolved among ourselves without becoming public. Obviously, there is someone behind the scenes who quickly spreads the story, and combined with a season without titles-where Madrid is always under the spotlight-everything gets blown out of proportion.
"Today we had another disagreement. During the argument, I accidentally hit a table, causing myself a small cut on my forehead that required a routine visit to the hospital.
"At no point did my teammate hit me, nor did I hit him, although I understand it may be easier for people to believe that we got into a fistfight or that it was intentional-but that did not happen.
"I feel that my anger about the situation, my frustration at seeing some of us reaching the end of the season on our last legs, giving everything we have, pushed me to the point of arguing with a teammate.
"I'm sorry. I'm sincerely sorry because this situation hurts me, and the moment we are going through hurts me. Madrid is one of the most important things in my life, and I cannot be indifferent.
"The result is an accumulation of things that ended in a meaningless fight, damaging my image and leaving room for doubt, invention, defamation, and embellishment of an accident. I have no doubt that any friction we may have off the field disappears on the field, and if I have to defend him inside a stadium, I will be the first to do so.
"I was not going to speak until the end of the season. We were eliminated from the Champions League, and I kept my anger and resentment to myself. We have wasted another year, and I was not in a place to make social media posts when the only face I needed to show was on the field-and I feel I did that.
"That is why it pains and saddens me more than anyone to go through this situation, which prevents me from playing in the next match due to medical decisions, because I have always gone until the very end, whatever the consequences. It hurts me more than anyone not to be able to do so. I am at the club's and my teammates' disposal to cooperate with whatever decision they deem necessary."
