It happened at 1:25 p.m. at the Wilmington Savings Fund Society bank branch at the corner of Delaware Avenue and Washington Street.
Police say the man held up the bank and fled.
A short time later, officers spotted a man matching the description of the bandit at 9th and Jefferson Streets.
They quickly took him into custody.
Officers at the scene told Action News that items stolen from the bank were found in the man's possession.
The investigation continues.