The teen, who has not been identified because of his age, was arrested in Wilmington on Monday.
The robbery happened at 3:15 p.m. Wednesday at the a bank inside a grocery store.
Police say the teen gave a demand note to a teller, who turned over an undisclosed amount of cash.
A weapon was not displayed, police said, and the teller was not hurt.
The teen was charged with robbery and was sent to the New Castle County Juvenile Detention Center.