The 27-year-old has a history of knee problems, having first suffered a torn ligament while playing for Villarreal in October 2011 and repeating the injury in April 2012.
Rossi then suffered a ligament strain in January of this year, which ultimately contributed to him missing the World Cup with Italy, and the former Manchester United youngster has now undergone yet another operation after aggravating his knee during training.
Fiorentina confirmed via their official website on Friday that Rossi had undergone surgery in Colorado, insisting that the previous treatment still showed signs of "good stability". They also revealed the player is estimated to return to action within four to five months, after recovery work in both New York and Florence.
Rossi managed 16 goals in 22 Serie A appearances last season despite his fitness problems.