The controversial defender did not sustain any serious damage in Sunday's draw against Valencia, but will sit out Thursday's game with Barcelona as a precautionary measure.
The center back picked up the knock in his side's 1-1 draw with Valencia on the opening weekend of the Liga season, and spent Sunday night in hospital undergoing a series of examinations.
Even though all the tests came out negative, Pepe will not feature in the first leg of the Supercopa Espana tie against Barcelona on Thursday, but he has vowed to pay everybody back for their support.
"I appreciate the many displays of support that I have been shown in the last few days," Pepe told reporters. "I am flattered by the encouragement I have received since Sunday, especially from the fans of Real Madrid. I will be in perfect shape very soon to continue fighting for the [Madrid] jersey.
"I also want to thank, in particular, the team doctors, who have been and remain by my side at all times. I thank all of my colleagues from other clubs for being interested in my health. These small details have not been missed. I send a big hug to everyone."
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