The Spanish club said tests done on Friday showed that the France international has a "grade 2 injury" in his left thigh.
Varane was hurt during Real's 2-1 defeat at Valencia on Wednesday, the club's second loss in La Liga.
Real said Varane's "recovery will continue to be assessed," but he is likely to be sidelined for about three weeks.
Varane has started in 18 league games for Real and made seven Champions League starts.
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Real are one point clear of Barcelona at the top of La Liga with a game in hand and hold a 3-1 advantage over Napoli from the first leg.
(Reporting by Adriana Garcia; Editing by Louise Ireland)
