Pepe could miss key games in La Liga and Europe this month after fracturing two ribs against Atletico Madrid on Saturday.
The centre-half scored the opening goal in the Madrid derby before a collision with team-mate Toni Kroos ended his afternoon prematurely.
Antoine Griezmann scored a late equaliser after Real's reshuffle, and there was more bad news from the hospital in the hours after the game.
A Real statement read: "The player has been diagnosed with fractures to his seventh and eighth left ribs. His recovery will continue to be assessed."
Real take on Bayern Munich over two legs in a Champions League quarter-final this month and face a potential title-deciding Clasico against Barcelona on April 23.
Zinedine Zidane is currently without defender Raphael Varane, sidelined with a hamstring injury, leaving Nacho in line to come in alongside Sergio Ramos in Munich on Wednesday.