The Brazilian was an unused substitute in Real's 5-0 demolition of Rayo Vallecano on Saturday, but has since sustained the injury to his left leg.
No recovery time has yet been set by the club, but any kind of involvement in his the UEFA Champions League quarter-final clashes with Borussia Dortmund now appears unlikely, and he could also be a doubt for the Copa del Rey final versus Barcelona on April 16.
Marcelo has made 33 appearances in all competitions for Real this season.
Carlo Ancelotti's men sit third in La Liga, three points adrift of leaders Atletico Madrid and two short of Barcelona.
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