Real Madrid say defender Pepe broke two ribs in his left side during Saturday's 1-1 draw with Atletico Madrid.
Pepe, who scored Real Madrid's goal, left the match in the 67th minute after receiving a knock, and the club later confirmed the injury, saying the Portugal international's return to action will depend on the speed of his recovery.
"Following the tests carried out on Pepe at the Sanitas la Moraleja University Hospital, the player has been diagnosed with fractures to his 7th and 8th left ribs," a club statement said. "His recovery will continue to be assessed."
Real Madrid are heading to Bayern Munich for the opening leg of their Champions League quarterfinal on Wednesday, with El Clasico against Barcelona set for April 23.
The 34-year-old Pepe's contract is up this summer, leading to speculation that his 10-year stint in the Spanish capital is coming to a close.
Madrid were already without another centre-back as Raphael Varane missed Saturday's match with a muscle injury.