La Viola confirmed the Italy international had suffered a "sprain" to his right knee, the joint in which he has twice damaged cruciate ligaments.
He was replaced in the 71st minute of the match.
A club statement read: "Fiorentina announce that following a challenge from Livorno player Leandro Rinaudo, Giuseppe Rossi suffered a sprain to the knee that had already been operated on.
"Tomorrow more tests will be performed."
Rossi missed almost two seasons after two cruciate ligament injuries while at former club Villarreal, but has recovered to lead the Serie A scoring charts this season with 14 goals.
He has also returned to the Italy squad.
"We are all worried about Rossi. Tomorrow there will be the necessary medical tests," Montella told Sky Sport Italia.
"We are above all sad for his state of mind. It's a real shame, as the foul seemed to be intentional and the player behind it didn't even apologise. Usually when someone commits a foul like that you say sorry, as there was no way Rinaudo was going to get that ball."