The CBI said the 14 banks have the freedom to use the Iraqi dinar and other non-US dollar currencies.
The Wall Street Journal reported the ban, which was imposed by the Treasury Department and the Federal Reserve Bank of New York as part of a crackdown on the siphoning of US currency to Iran.
The US uncovered information that Iraqi banks were allegedly involved in money laundering and fraudulent transactions, the newspaper said.
"We have strong reason to suspect that at least some of these laundered funds could end up going to benefit either designated individuals or individuals who could be designated," a senior US official reportedly said.
"And of course the primary sanctions risk in Iraq relates to Iran."
Among the banks on the US ban list are Al Mustashar Islamic, Erbil, World Islamic and Zain Iraq Islamic Bank, the newspaper added.
Iraq's private banks association did not immediately respond to a request for comment by Reuters.
The ban is part of a wider crackdown by Washington on US dollar transactions in Iraq.
In November the CBI started preventing several Iraqi banks from dealing in US dollars.
Measures taken by the US this year to stamp out money laundering and the channelling of dollars to Iran and Syria from Iraq have severely restricted Baghdad’s access to hard currency.
Since the US invasion of Iraq in 2003, Iraq’s foreign currency reserves have been housed at the US Federal Reserve, giving Washington significant control over Iraq’s supply of dollars.
Iran has been unable to access billions of dollars in assets in several countries due to US sanctions.