Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
There are two types of Islamic banks:
First: Sharia-compliant where specialized committees are in charge of supervising various transactions and developing policies. It is permissible to work for this type and the given wages are lawful.
Second: Sharia-non-compliant where transactions aren`t supervised by any committee and staff member is entrusted with tasks that violate the teachings of Sharia. It isn`t permissible to work for this type under the cloak of "Islamic Bank." And Allah the Almighty Knows Best.