"Medical examinations this morning determined Robben has a Grade II tear on his right leg's soleus muscle," the Spanish champions said in a statement on their website.
"He won't be able to play for five or six weeks."
The injury-prone Robben played just 26 matches for Real since joining from Chelsea in the summer of 2007.
The 24-year-old's repeated injuries left Real Coach Bernd Schuster with few options on the flanks, especially after the departure of Robinho to Manchester City.
The German tactician had to field Royston Drenthe as a left-winger in Wednesday's 2-0 Champions League defeat to Juventus at Santiago Bernabeu.
Argentinean forward Gonzalo Higuain played that role during the past few matches in the Primera Liga.
Watch Robben's best moments