Modric was taken off on the hour mark following a challenge with Recio in Saturday's 3-1 win over Malaga at Santiago Bernabeu.
A statement on Real's official website read: "Following tests carried out on Luka Modric at the La Moraleja Sanitas Hospital by Real Madrid Medical Services, he has been found to have a strain to the medial collateral ligament of his right knee. His situation will be monitored."
The victory for Carlo Ancelotti's side came at a cost, with forward Gareth Bale going off after just five minutes with an apparent calf problem.
No update has been provided on the extent of the Wales international's injury, although he is almost certainly a doubt for the UEFA Champions League quarter-final second leg with city rivals Atletico Madrid on Wednesday.
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