The 31-year-old, who joined PSG in 2013 and has made over 300 Ligue 1 appearances, picked up the injury days before Wednesday's Champions League clash at Barcelona, with Joao Neves, Desire Doue and Ousmane Dembele also injured.
Neves, Doue and Dembele are continuing their rehabilitation, PSG added in a statement.
Marquinhos suffered the injury late in Monday's 1-0 loss at Olympique de Marseille, PSG coach Luis Enrique said.
"He told me he felt a little pain. Nothing important, but we just need to be attentive and not take any risk," Luis Enrique told reporters on Friday.
"It's a shame for us because Marquinhos is our captain, but we have to be ready, and I think we are."
The PSG coach said he was not worried about the injuries.
"Football is a sport where injuries are normal because there's impact. It's an impact sport. It's normal to have muscle injuries, and we have to know how to manage that," he added.
"We have plenty of players from the academy that can play."
Champions PSG will host Auxerre in a Ligue 1 clash on Saturday.