The thieves got hold of $6.5m in Iraqi dinars, a day after the money was transferred to the bank.
Police suspected the robbers got help from an inside source, as bank guards working on the overnight shifts were instructed not to open the doors for any senior officials.
A detective told the news agency AFP that there were two likely scenarios: one guard could have been helping the robbers, who then decided to kill him, or a guard working on another shift at the bank may have convinced his colleagues to open the door for the gang.
Investigators believe the gunmen used silencer-fitted weapons during the attack.
"It was all done in a professional manner," a police officer said.
Another official said the robbery appeared to be the work of armed groups trying to get hold of cash to finance their operations.
"This operation was carried out by a terrorist element who lost their foreign funding... and started to seek internal funding, like stealing from banks," the police officer told the news agency AFP.
The raid came after five people were killed on Sunday in a daylight attack at a popular money exchange office, a reflection of the increasing crime in Iraq even as violence is on the decline.
The gunmen broke into the al-Nibal money exchange office in downtown Baghdad shortly before noon, killing three employees and two customers, said Iraqi police officials.
They said 12 others, including eight employees, were wounded in the attack in Baghdad's commercial Karradah district.