Rossi, 30, tore the anterior cruciate ligament in his left knee during Celta's 2-0 defeat at home to Eibar on Sunday, six days after scoring a hat-trick for the Galicians in a 3-0 win over Las Palmas.
The striker, who made his professional debut with Manchester United, tore the anterior cruciate ligament in his right knee twice in the 2011-12 season with Villarreal, and again in 2014 with Fiorentina.
Rossi is still owned by Fiorentina and looked to be on the way to resurrecting his stricken career after a successful loan spell at Levante last season which earned him another loan move to Celta.