The goalkeeper suffered a knee injury last week and has since undergone surgery.
Barca announced on Saturday: "Joan Garcia underwent surgery this morning at the Barcelona Hospital for a torn internal meniscus in his left knee. Dr. Joan Carles Monllau performed an arthroscopy.
"It will be confirmed that the recovery time will be reduced to between 4 and 6 weeks, depending on the evolution of the condition."
Barca coach Hansi Flick said on Saturday: "We don't like not being able to count on Joan, obviously. He's done a great job so far, but these things happen.
"(Wojciech) Szczesny? In the second half of last season, we won almost every game and three titles with him. He's a fantastic goalkeeper and person, I have no doubt about it."
