
Babacar, 22, was on the pitch for just seven minutes in Fiorentina's 1-0 home defeat to Verona on Monday before being forced off, and a scan on Tuesday showed he had suffered ligament damage.
A Fiorentina statement said: "Tests revealed a grade-two strain to the medial collateral ligament in Babacar's right knee."
Boubacar's absence is a blow for Vincenzo Montella's side, who have been without Giuseppe Rossi all season after he ruptured knee ligaments in the summer.