Dzeko sustained the injury in Roma's 1-1 draw at home against Cagliari on 7 October (AEDT), ruling him out of international duty for Bosnia-Herzegovina in its UEFA Euro 2020 qualifiers against Finland and Greece.
Pesucci revealed that the 33-year-old's injury is worse than first thought and would not be able to return until 24 October when Roma faces Borussia Monchengladbach.
He advised Dzeko should be among the substitutes for that UEFA Europa League clash, ready to make a full return to first-team action three days later against AC Milan
"It was a bad break," Pesucci told Corriere dello Sport.
"Initially, only the zygomatic arch seemed broken, but then we also found a fracture at the lower edge of the right eye's orbit.
"Osteosynthesis was necessary, with the use of a plate fixed by screws to stabilise the orbit. Only in this way could the fracture of the zygomatic arch be contained.
"In other cases, I have worked on isolated fractures. Edin's is more complex, because it is a double and therefore the stabilisation will take longer."
Dzeko will be missed by Bosnia, having scored two goals in two games as it beat Liechtenstein and lost to Armenia in September.
He has also scored four of Roma's 12 Serie A goals this season as it sits fifth on the table.
Pesucci added: "He must not be in a hurry. Edin still has pain. He had the operation on Monday, and he must feel comfortable for a week."