The 20-year-old left the pitch in the 62nd minute during the 1-1 draw in Lorient on Wednesday, after halting his run and screaming out in pain. He was then carried off on a stretcher before leaving the stadium on crutches.
"Further review of the injury will take place after the international break," PSG said in a statement.
Doue will miss next week's Champions League clash against Bayern Munich and France's upcoming World Cup qualifiers in November.
"It's always bad news when there are injuries," PSG manager Luis Enrique told a press conference on Wednesday. "It's a strange injury."
The forward had only recently returned from a calf injury that had sidelined him for six matches with PSG and the previous set of World Cup qualifiers for Les Bleus.
Doue has scored three goals and registered one assist this season in all competitions.