The 25-year-old attacking midfielder sustained the injury in training ahead of Thursday's Europa League defeat by Hoffenheim and will require surgery.
Sulc was the team's second-leading scorer last term with 14 goals, 11 of those in Ligue 1. He has scored twice in 10 games in all competitions this season.
"We lost Lois (Openda) for a few weeks, and now we lose Pavel," said Lyon captain Corentin Tolisso.
"We knew how important he was, just like Lois, and of the impact he brought to our game as soon as he arrived. They're players we're really going to miss."
Lyon began the weekend as one of five teams level on points at the top of the table. Paulo Fonseca's side are in first place on goal difference ahead of Monday's trip to Paris Saint-Germain.
The match was pushed back from Sunday following a request by police amid a wave of violent protests in the French capital.