The Japan international will almost definitely also miss the Asian Cup, which takes place between January 12 and February 10 in Qatar.
Mitoma was forced off towards the end of the 1-1 draw with rivals Crystal Palace on 21 December and was later pictured leaving Selhurst Park on crutches.
"We’ve lost Kaoru for around four, five or six weeks," De Zerbi said ahead of tonight's match with Tottenham.
"We have more or less 10 injured players, maybe less, maybe eight, but two players can’t start the game."