Abdel Razzaq Mansur, the chief executive of Babylon Bank, said the branch which opened on Sunday had so far worked with 50 clients and expected to be dealing with about 200 within a year.
"In Najaf, there are many women who are business women, and they have companies in many different lines of work," he said, noting the branch's 25-strong staff were composed entirely of women.
The only men working for the branch were special security guards stationed outside the bank on the street, Mansur said.
It will provide loans, investments, deposits and savings in both Iraqi dinars and US dollars.
Asked whether any men would be allowed to enter the branch, he replied, while laughing: "I am the boss, but I can only ask them to come here (to Baghdad) -- I can't go there."
Mansur added that while he hoped to expand the concept to Baghdad, Babylon Bank would not extend it beyond Najaf for now.
Najaf, located 150 kilometres (90 miles) south of Baghdad, is home to the mausoleum of Imam Ali, the son-in-law and cousin of the Prophet Mohammed, which attracts Shiites from around the world, particularly neighbouring Iran.