The Brazil international was forced off against the Corsicans after 57 minutes, and will not return to match action until February 8's clash with Bastia.
"The point of the day was a medical update regarding Thiago Silva, who was released due to injury in the 57th minute of the match Ajaccio," a statement on the club's official website confirmed.
"The MRI that was performed today confirms a femoral biceps injury in the left leg. He will be unavailable for an estimated three weeks at the minimum."
Friday's 0-0 draw saw les Parisiens concede top spot in Ligue 1 to Olympique Lyonnais.