Clerc, who is the Heineken Cup's all-time top try scorer and has more Test tries to his name than any other Frenchman still playing, pulled up late in the second half of Toulouse's 19-14 win at Stade Ernest Wallon on Friday and was unable to finish the match.
The severity of the injury is still not clear but Clerc confirmed that he feared a muscle pull.
It has been a hard week for Les Bleus injury wise, as they have already lost centre Gael Fickou and full-back Brice Dulin.
France head coach Philippe Saint-Andre has called Toulouse's Maxime Medard into his squad as a replacement for the injured Dulin.
The 22-year-old has been ruled out of the entire tournament after incurring an adductor injury in Castres's defeat to Bayonne on Thursday.
Medard, who has 31 caps for France, returns to the national side for the first time since sustaining a serious knee ligament injury against Scotland in last year's Six Nations.
France begin their Six Nations campaign against Italy in Rome on Sunday February 3.