The 27-year-old Italian international recently suffered a recurrence of the ligament problem that saw him miss the World Cup.
Having seen a knee specialist in Colorado, Rossi is now expected to be on the sidelines until the start of 2015.
"The athlete will be monitored in Vail this week. At the end of the activity will begin physical therapy in New York, which will continue in Florence," read a statement on Fiorentina's official website.
"Resumption of sports activity will be dictated by the specialist, which is estimated at around four to five months."
Rossi scored 17 goals in 23 appearances for Fiorentina last season.