The Belgian international "has successfully undergone surgery today to repair the torn anterior cruciate ligament in his left knee," Real said in a brief statement.
The club added that Courtois will start his recovery programme "in the coming days" but did not specify how long it would be before he is able to play again, amid fears that he may be out for almost the entire season.
Courtois was injured in training a week ago and his long-term absence led Madrid to recruit Kepa Arrizabalaga, who was introduced on Tuesday after joining on a season-long loan from Chelsea.
Brazilian defender Eder Militao, who suffered the same injury as Courtois in Saturday's 2-0 win in their La Liga opener against Athletic Bilbao, will also have to undergo surgery shortly.
Young midfielder Arda Guler underwent successful surgery on Monday for a meniscus injury in his right knee. He is expected to be out of action for the next six to eight weeks.
