About a quarter of the roughly 300 Islamic lenders worldwide are reported to have less than $25m in paid-up capital.
Kamel said: "There is a need for this mega-bank to make the tools to increase liquidity in Islamic banks, and move the banking system more towards Sharia [Islamic law] goals."
A ban on charging interest and investing in prohibited businesses such as trading in alcohol, pork, arms, pornography or gambling, are among features distinguishing it from traditional banking.
The bank, named Emaar, will have an initial capital of $1bn provided by financial institutions.
Albaraka Banking Group, which Kamel also chairs, will be one of the founding investors.
Adnan Yousif, Albaraka's chief executive, said Emaar would be founded in Bahrain within two months.
Shares in the bank will then be offered in two tranches, the first taking the bank's capital to $10bn, and the second to $100bn, in a process that will take five to seven years, Kamel said without giving further details.
The other Islamic financial institution involved in setting up Emaar is the Islamic Chamber of Commerce and Industry, said Ezzedine Khoja, secretary-general of the General Council.
Khoja said a timeline for the second and third tranches of investment had not yet been decided, or the how investments will be solicited.
A tripling of oil prices in the five years to July has flooded the Islamic finance sector with petrodollars, accelerating its expansion.