"We are opening the bank today and are beginning to offer our services to the public," Alaa al-Rafati, head of the National Islamic Bank, told AFP.
The National Islamic Bank has $20 million in start-up capital and will operate under Islamic finance rules, he said.
With offices on four floors of a building in central Gaza City, the bank will hold the accounts of 6,000 Hamas employees whose salaries are to be deposited in the bank.
Rafati did not say how the Islamist movement acquired the start-up capital in a territory under Israeli embargo since Hamas, which is pledged to the destruction of the Jewish state, violently seized power in 2007.
Because of the blockade, which has prevented all but essential humanitarian goods from entering the territory, Gaza's banks have faced a virtually constant liquidity crisis.
Rafati said no such problems would plague the new bank.
"We have absolutely no crisis of liquidity, be it shekels or dollars. This will allow us to win the confidence of customers."
Although the vast majority of the board of directors are members of Hamas, including Rafati, he said the bank was "a private enterprise aimed at making profit and is not associated to Hamas or to the government in Gaza."
The Palestinian Authority - which Hamas loyalists booted out of Gaza in a week of deadly street fighting in June 2007 - has refused to issue the bank a licence and called for it to be boycotted.
The Gaza Strip has been outside the control of the PA and Palestinian president Mahmud Abbas since the Hamas takeover.