The Brazilian full-back, who has been on international duty in North America over the past week underwent tests on Thursday morning which revealed a tear in his soleus muscle.
Alves joins a lengthy injury list at Camp Nou , with Victor Valdes, Jordi Alba, Gerard Pique, Cesc Fabregas and Lionel Messi also ruled out.
He is set to miss his side's fixtures against Granada in La Liga and Ajax in the UEFA Champions League, but is hopeful of recovering in time for the trip to Athletic Bilbao on December 1.
The 30-year-old has made 15 appearances in all competitions for Barca this season, scoring two goals.
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