Jordan's King Abdullah II ordered that Shoman's body be laid to rest at a royal cemetery, and funeral arrangements were set for Wednesday, the state Petra news agency reported.
Shoman was admitted to an Amman hospital a month ago, complaining of fatigue, and died at the hospital on Tuesday, a bank official said.
Shoman hailed from a prominent Palestinian family from the West Bank town of Bait Hanina. His father, Abdul-Hamid Shoman, established the first branch of the Arab Bank in Jerusalem in 1930.
The bank was a symbol of Palestinian aspirations, representing a drive to create financial institutions for a new nation.
Following Israel's seizure of the West Bank, including Jerusalem's traditional eastern Arab sector, the Shomans moved to Jordan, where they set up branches for their bank across the Arab kingdom.
Under the late Palestinian leader Yasser Arafat, the Palestine Liberation Organisation kept a large part of its funds in the Arab Bank.
The Arab Bank now has more than 30 branches across the Middle East, Europe, the United States, Australia and North Africa. Trading in its shares often leads the Amman Stock Exchange.
Shareholders in the Arab Bank include the Saudi Oger Co, owned by the late Lebanese prime minister Rafiq al-Hariri who was killed in a car bomb in February.