The near-simultaneous blasts occurred shortly after 11am on Sunday in the Yarmouk neighbourhood in western Baghdad.
Iraqi security forces say suicide bombers drove two cars laden with explosives to the bank, then detonated them.
"Each car was loaded with 80 kilogrammes of ammonium nitrate," the Baghdad operations command said.Five bank guards were killed in the explosion, and six others were wounded, according to Hussein al-Uzri, the bank's chairman.One of the two bombs exploded near an office of Iraq's interior ministry where Iraqis apply for their national ID cards. Many of the victims from that blast were women, according to the Iraqi army.
The Yarmouk district is not far from Baghdad's heavily-guarded Green Zone. The bank is one of the public sector's most active financial institutions and has been working to encourage foreign investment in Iraq.
Banks have become frequent targets for both criminals and fighters in recent months. A June 13 raid on Iraq's central bank killed 15 people which the security forces blamed on the remnants of al-Qaeda in Iraq. And gunmen stole $6.5m from a Baghdad bank last summer.
Sunday's bombings occurred after a string of attacks in the capital on Saturday evening.