Federico Valverde suffered a head injury on Thursday in an altercation with teammate Aurélien Tchouaméni.
What happened?
The incident occurred during a training session ahead of the weekend match against Barcelona.
Valverde downplayed the incident, saying no punches were thrown and he hurt his head after accidentally hitting a table.
Why it matters for Federico Valverde
The 27-year-old midfielder's injury could keep him sidelined for the final four games of the domestic season.
Real Madrid said Valverde has been diagnosed with a cranioencephalic trauma and will need to rest for 10 to 14 days.
What comes next?
Valverde apologized for the altercation, saying everything has been blown out of proportion after a frustrating and lengthy season.
The team gave no timeline on the disciplinary proceedings against Valverde and Tchouaméni.
Valverde is a key midfielder for Uruguay, which will play in Group H at the World Cup, with their first game against Saudi Arabia on June 15.
The incident is the latest disruption to a Madrid squad that has endured a tough season, including lackluster results and fan criticism of stars.
Madrid could see Barcelona celebrate the league title in Sunday's clasico at the Camp Nou, with the Catalan club needing only a draw to win its second league title in a row.
Valverde's injury is a significant blow to Madrid's chances of finishing the season strongly.
The club will provide updates on the resolutions of both proceedings once the corresponding internal procedures have been completed.
There was no reported injury to Tchouaméni, a 26-year-old France international who has not commented publicly on the incident.
Defender Álvaro Carreras confirmed on Instagram that he was involved in an incident with a colleague, which he described as minor and isolated.
Spanish media reported that Carreras and defender Antonio Rüdiger got into a scuffle during one of the team's training sessions.
Madrid is set to finish the season without winning any major title, having been eliminated by Bayern Munich in the quarterfinals of the Champions League.
The team was also ousted by second-division club Albacete in the round of 16 of the Copa del Rey and finished as runner-up to Barcelona in the Spanish Super Cup.