The summer signing from Bayern Munich hurt his knee during Fiorentina's 1-1 draw at home with Cagliari on Sunday.
Scans have confirmed the extent of the damage, which has caused a partial lesion of the collateral medial ligament.
Gomez will now spend two weeks wearing a brace before starting his rehabilitation and it is likely to be the end of October at the earliest before the Germany international is ready to return.
The Viola have also stated that Juan Cuadrado will be out for three weeks after suffering a dislocated shoulder in the same game.
Fiorentina owner Andrea Della Valle said: "It felt as though we were cursed in this game. I am sorry that Cuadrado got hurt.
"We hope to recover both players as soon as possible."
Fiorentina host Portuguese side Pacos Ferreira on Thursday in their Europa League Group E opener before travelling to Bergamo to face Atalanta this weekend.