The Bardiani Valvole - CSF-Inox rider fractured his right scaphoid after hitting a step.
He went to hospital shortly before the team time trial on stage two and X-rays confirmed the break.
Modolo, 25, said: "Due to a distraction, I fell down trying to rider over a step.
"I'm sorry for the team. I arrived here with a good shape and the aim to achieve some good results in Qatar and then in Oman. Now I have to recover as quickly as possible and reschedule the first part of season from scratch."
Modolo will now return to Italy to continue training off the bike.