He will undergo arthroscopic surgery on his right knee on Monday in a bid to repair damaged cartilage.
Silvestre first complained of soreness in his knee during fitness tests with the German club on Wednesday.
Werder Bremen's physiotherapist, Dr. Gotz Dimanski, said: "The intensive studies at Augsburg knee specialist Dr. Ulrich Boenisch confirmed our suspicions that there is a cartilage defect in his right knee.
"This will take several months of rehabilitation."
Silvestre's injury has worsened the existing injury crisis at the club, particularly affecting their defence.
The 33 year-old joins Per Mertesacker and Naldo on the sidelines, while Sebastian Prodl and Sebastian Boenisch are also unavailable through injury.
Mertesacker said: "I want to be fit again as soon as possible. It is my entire focus."
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