The 29-year-old picked up the knock in the latter stages of the match, but test results revealed that no lasting damage had occurred.
"I appreciate the many displays of support that I have been shown in the last few days. 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," Pepe told reporters.
"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 give out a big hug to everyone."
Pepe will miss Thursday's Spanish Supercopa clash with Barcelona.