Real did not say how long the 32-year-old would be out of action but local media reported he was likely to be sidelined for around 10 days.
He will probably miss the La Liga games at home to Granada on Sunday and at Rayo Vallecano three days later but should be available for the match at home to Eibar on April 11.
"Following medical tests carried out on Pepe by the Real Madrid doctors in the Sanitas La Moraleja Hospital, he has been diagnosed with an injury in the vastus internus muscle in his right thigh," Real said on their website.
"His progress will be monitored," they added.
Real are second in La Liga with 10 games left, four points behind leaders Barcelona.
France defender Raphael Varane is likely to partner Spain's Sergio Ramos in central defence in Pepe's absence.
(Reporting by Iain Rogers, editing by Toby Davis)
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