The 29-year-old suffered the setback in a 1-1 draw with Monaco last month and could return for PSG's UEFA Champions League clash against Anderlecht next Tuesday.
Silva will sit out Friday's Ligue 1 clash against Lorient, with coach Laurent Blanc keen to be careful with the Brazil international to diminish the risk of future injuries.
"This is not a trivial injury. With him, we must be very careful. I am very happy for him because six weeks is a long time," he said.
"This is someone who trains very well and has a healthy lifestyle."
The centre-back, who joined PSG from Milan at the start of last season, started 22 league games for the capital club in their title-winning campaign last term.
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