The Italy international will undergo surgery later this week on his right knee after tests revealed signs of excessive pressure being put on that joint.
The Viola are hopeful that the 27-year-old striker, who has already undergone two operations to reconstruct cruciate ligaments in that knee, will not be sidelined for long.
"We love Rossi for who he is, not just the player," Fiorentina sporting director Daniele Prade said to www.acffiorentina.it. "To know that he is still not well makes us feel bad.
"He (Rossi) must check how his meniscus is and we are anxious but we have to be optimistic regarding his recovery."
Rossi missed four months of last season with a right knee injury before returning to play in May.
The former Manchester United striker still finished as the team's top scorer with 16 goals.
"Rossi is very optimistic," Fiorentina technical director Eduardo Macia said to www.acffiorentina.it. "He has an extraordinary mentality, that of a champion, and this is why we are calm.
"He never gives up and he will continue to give so much satisfaction to Fiorentina.
"His only focus right now is to return as soon as possible to be 100 per cent."
Fiorentina, coached by Vincenzo Montella, will take on PAOK Salonika, Guingamp and Dinamo Minsk in Group K of the Europa League.