The 34-year-old -- who won two league titles with Nantes in 2001 and Lille in 2011 -- picked up the problem in the 3-0 defeat by Marseille in their Ligue 1 clash on Saturday.
He is due to miss Ligue 1 games against Monaco, Saint-Etienne and defending champions and leaders Paris Saint-Germain.
Landreau is currently third in Didier Deschamps' pecking order to keep goal for France at the FIFA World Cup™ in Brazil behind Tottenham's Hugo Lloris and Steve Mandanda of Marseille.
Landreau has 11 caps to his name. He made his debut in the 2001 FIFA Confederations Cup, and was a member of the French squad that reached the 2006 FIFA World Cup final, although coach Raymond Domenech didn't give him any playing time.
After falling out of favour - he was overlooked for UEFA EURO 2008 - he earned a recall in 2012 from Deschamps, with Cedric Carrasso making way.