Camavinga, 21, was taking part in a training session with the national team on Wednesday when he picked up the injury in a challenge.
He returned to Madrid for tests, and underwent a further scan on Friday to determine the extent of the problem.
"Following tests carried out today on our player Eduardo Camavinga by the Real Madrid medical services, it has been diagnosed that he has torn the lateral collateral ligament in his right knee," Madrid said in a statement. "Further developments are awaited."
Camavinga joined Madrid from Rennes in August 2021 and has become an important member of the first team.
He has featured in all 13 of Real Madrid's LaLiga matches this season, starting nine and appearing in the other four as a substitute.
Madrid's squad has been hit by a series of injuries in recent days, especially in midfield.
Jude Bellingham is currently absent with a shoulder problem, Aurélien Tchouaméni has a broken bone in his foot, goalkeeper Kepa Arrizabalaga is absent with a thigh injury and forward Vinícius Júnior was hurt in Brazil's defeat to Colombia on Friday.