The 23-year-old, who scored his first Ligue hat-trick earlier this month, picked up the injury during training.
Ninga was stretchered off in tears.
The African forward is Montpellier's top scorer this season with five goals in the past two matches, to help move the club away from the relegation zone in 15th place.
He scored seven last season after arriving in the summer of 2015 from Gabon club Mangasport for 75,000 euros ($82,000).