Rossi limped away shaking his head after a rough tackle by Livorno defender Leonardo Rinaudo in the 71st minute.
Rinaudo was booked and was lucky not to be sent off after he argued with the referee and his opponents, leading to a series of pushes among the players.
Rossi, previously with Villarreal in Spain, has come storming back this season with 14 league goals after recovering from successive anterior cruciate ligament injuries to his right knee which effectively cost him two years of his career.
There was no immediate word on the extent of the injury.
The win lifted Fiorentina to joint third alongside Napoli, who host Sampdoria on Monday, on 36 points from 18 games.
Earlier, Cagliari forward Mauricio Pinilla missed a penalty, sending a wild kick high and wide of the goal, as his side drew 0-0 at Chievo in a match which kicked off the weekend programme.
The two games served as an appetiser for the top of the table clash between leaders Juventus and second-placed AS Roma (1945 GMT). The other seven matches will be played on Monday, which is a bank holiday in Italy.