The Spanish club said in a statement that Navas had been diagnosed with a "swollen adductor muscle in his right groin".
Spanish media reported that the Costa Rican was not set to feature against Getafe in La Liga on Saturday and may not be back in time for the European clash at the Santiago Bernabeu three days later.
Navas sustained the injury while on international duty with Costa Rica, whom he helped reach next year's World Cup thanks to a 1-1 draw against Honduras on Saturday.
Real Madrid have suffered various injury problems already this season and are also without former Spurs winger Gareth Bale, right back Dani Carvajal and midfielder Mateo Kovacic.
(Reporting by Rik Sharma; Editing by Toby Davis)
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