Tests done on the Germany international showed Gomez has a sprained right knee and has partial lesion of the collateral medial ligament.
Gomez will undergo further examinations later this week once the swelling subsides to confirm the recovery time.
"I am worried about Gomez even though I don't think it is a very serious injury," Della Valle said on the club's official website.
Gomez, who joined the Tuscan outfit on a 20million euros transfer deal from Bayern Munich this summer, is expected to be out of action for at least six weeks.
Fiorentina coach Vincenzo Montella also lost Juan Cuadrado to injury in Sunday's game.
The Colombian winger dislocated his shoulder and will be on the sidelines for two weeks.
"It felt as though we were cursed in this game," Della Valle said."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.