Kurzawa was substituted with 12 minutes to play during France's 1-1 draw with Sweden on Tuesday, and is now set for a lengthy period on the sidelines.
The 22-year-old has started 10 games for Leonardo Jardim's side this season, but the Portuguese coach revealed they will have to find another option in defence in the coming weeks.
"He has a muscular lesion in the left thigh which will require four to six weeks of treatment before he can return to competition," the head coach said.
"This is the second player who returns injured from international duty this season.
"But we will find a solution to overcome the lack of Layvin."
There was some positive news for Monaco ahead of their Ligue 1 clash with Caen, though, with Jardim confirming winger Yannick Ferreira Carrasco's return to training after a heel complaint.
The 21-year-old has scored two goals in his three league matches for Monaco before picking up the injury.
