The 29-year-old pulled up with what initially looked to be a groin problem in the 28th minute of Croatia's 1-1 Euro 2016 qualifying draw with Italy on Sunday.
Mateo Kovacic came on to replace Modric, and Real confirmed on Monday that the player would face further tests before a timeframe could be placed on his recovery.
A statement on the club's official website read: "After the imagining (sic) tests carried out by the Real Madrid Sanitas Medical Service on Luka Modric, a tear of the left proximal rectus femoris tendon has been found. Pending a medical evaluation."
Modric has made 10 league appearances for Real this season, scoring one goal.
His appearance against Italy represented his 83rd cap for Croatia.
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