The 28-year-old PSG and Brazil captain picked up the injury in the 1-1 home draw against Monaco in Ligue 1 on Sunday and had to be replaced after 15 minutes.
"I have bad news, although it could have been worse. After examinations, doctors told me I'll be sidelined for six weeks," Silva wrote on his Instagram feed on Tuesday.
Silva is suffering from the same kind of injury ruled him out for almost two months last season.
PSG coach Laurent Blanc told a news conference: "The injury is important. It's not the first time it has happened to him, so he knows that he will have to be patient".
Silva is set to miss two Champions League Group C games - next Wednesday's clash with Benfica at the Parc des Princes and the visit to Anderlecht on Oct. 23.
He is set to be replaced by compatriot Alex, who is back in the squad for Wednesday's Ligue 1 trip to Valenciennes. The French champions are second with 12 points from six games, two points behind Monaco after the pair drew 1-1 on Sunday.
The 2014 World Cup hosts Brazil are scheduled to play friendlies against South Korea in Seoul on Oct. 12 and Zambia three days later in Beijing.