Grange, 24, suffered the problem in a training session on Wednesday.
Further tests on Thursday showed a small tear to his right quadriceps.
Grange joined Nancy from Ligue 1 side Chateauroux in the summer and had become a regular starter in recent weeks, scoring once and getting two assists in his last four matches.
He had replaced Ziri Hammar in the team after the Algeria U21 international suffered a knee injury which required surgery. He will be out for a month.
Nancy are struggling near the foot of the Ligue 1 table.