It was unclear whether the attack was carried out by anti-government fighters, or whether the bombings were part of an attempted robbery.
Five bank guards were killed in the explosion, and six others were wounded, according to Hussein al-Uzri, the bank's chairman, who said the institution would still open for business on Monday.
"This attack on our headquarters in Baghdad... was an act of cowardice by malevolent forces who wish to undermine the progress that Iraq is making," he said in a statement.
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.
Heavily guarded area
|Many of the victims of Sunday's twin bomb blasts in Baghdad were women [AFP]
The Yarmouk district is not far from Baghdad's heavily-guarded Green Zone.
Al Jazeera's Omar al-Saleh, reporting from Baghdad, said the location of the attack would be viewed as another sign that the Iraqi army and police are struggling to provide basic security.
"If you walk 150 metres, you will have an Iraqi army checkpoint there," he said. "So it's kind of a blow to the security forces."
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.