At least three attackers struck the bank in Gardez, the capital of Paktia province, according to the provincial governor's office, and they were all killed at the scene. It said more than 10 people were also wounded in the assault.
An official at the city's hospital said they had received three dead bodies, including two police officers and one bank employee, and had treated 31 wounded people. It was not clear what had happened to the attackers' bodies.
There was no immediate claim of responsibility, and the attackers' motives were not immediately known.
Insurgent groups such as the Taliban and Islamic State often carry out attacks in Afghanistan, including in the past on banks, where police, soldiers, and other government employees routinely collect their paychecks.
On Wednesday, Islamic State claimed responsibility for a suicide attack on an Afghan state television station that killed at least six people as well as the attackers and wounded 24 in the city of Jalalabad.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)