The Portugal international was forced off just 16 minutes into Wednesday's Audi Cup loss to Bayern Munich at the Allianz Arena and is now a major doubt for Los Blancos' trip to Sporting Gijon on August 23.
"A medical examination on the player in the Universitario Sanitas La Moraleja hospital has shown that he has a muscle injury in his right leg," read a statement released on Madrid's official website on Friday. "His progress will be closely monitored."
Madrid face Valerenga in a friendly on Sunday before travelling to Asturia the following weekend to take on Sporting Gijon.
Coach Rafael Benitez has several other injury concerns at the moment, with both Cristiano Ronaldo and Karim Benzema having been left out of the squad for the Audi Cup.
Ronaldo is suffering with a minor back complaint, while fellow forward Benzema has a thigh problem.
Record signing Gareth Bale sat out Madrid's meeting with Bayern in Bavaria but Benitez insisted afterwards that the winger had merely been rested as a precautionary measure.
