At least 29 people were killed and nearly 50 others wounded in a car bomb in the provincial capital of Lashkargah, health officials confirmed.
Officials said military personnel and civilians had converged on the bank to draw their salaries ahead of Eid-al-Fitr when the bomb was detonated.
The incident happened at about 12 noon local time, a spokesman for the provincial governor Omar Zwak said.
The victims were taken to the emergency hospital, he added.
Earlier reports stated that gunmen had stormed the bank, however officials later retracted this and said the reported shooting had been carried out by security guards in the vicinity of the bank after the explosion.
No group including the Taliban has claimed responsibility for the attack.