The Brazil international was taken off with a little under 20 minutes left to play at the Bernabeu, as Los Blancos' slow start to the campaign continued.
Madrid have now released a statement outlining the extent of the damage, which reports in the Spanish press suggest will keep the 29-year-old on the sidelines until the end of October.
A club statement read: "Following tests carried out on Marcelo at the Sanitas La Moraleja University Hospital, he has been diagnosed with a grade two tear in his left bicep femoris muscle. His recovery will be monitored."
Marcelo is expected to miss league games against Deportivo La Coruna, Espanyol, Getafe and Eibar, as well as Champions League ties against Borussia Dortmund and Tottenham Hotspur either side of the international break.