It happened around 2:00 p.m. Friday at the M&T Branch located at 15 W. Lea Boulevard.
Investigators say a man walked into the bank, demanded money from the teller, then fled.
Police say the man did not display a weapon, but he did imply he had one.
Anyone with information is asked to contact the Wilmington Police Criminal Investigation Division, Detective McLaughlin at 302-576-3667.