The Spain international suffered the problem during the 5-2 defeat by Atletico Madrid on Saturday in La Liga.
Real Madrid did not specify an expected absence length, saying his "progress will be monitored" but Spanish media reported he will be out for around a month.
Los Blancos face rivals Barcelona in La Liga on October 26 at the Santiago Bernabeu.
Carvajal, 33, is also expected to miss Champions League games against Kairat and Juventus, and league clashes with Villarreal and Getafe, as well as Spain's upcoming World Cup qualifiers.
Madrid's other right-back Trent Alexander-Arnold is out with a hamstring injury and also a doubt for the game against Barca, with Fede Valverde an option to fill in there as he has done previously.
© 2025 AFP