The midfielder was taken off 17 minutes from time at the Stade Pierre-Mauroy, and Elie Baup's men went on to lose the game to a late Nolan Roux strike.
While a statement on Marseille's website confirmed he faced a lay-off of between four and six weeks, Baup is hopeful the France international can return sooner.
"As regards Mathieu Valbuena, if the recovery is good, he will be sidelined for a few weeks - you should speak to the doctor - three or four weeks maybe," Baup explained on Tuesday.
"Conceding a goal in stoppage time, along with our failure to score, and in addition to losing Mathieu, and perhaps Dimitri (Payet), who has a calf problem, it's (been) a tough night."
Payet was withdrawn 12 minutes from the end at Lille as Marseille's three-game winning streak in Ligue 1 came to an end.
They sit fourth in the league, eight points off Monaco who occupy the third and final UEFA Champions League spot.
