The 64-year-old man was shot in the head around 1 p.m. Monday at the Lancaster Market on Lancaster Avenue.
Investigators do not know a motive and they have not made any arrests.
They are planning to release more details, including the victim's name, after an autopsy is completed.
Anyone who may have information relative to this investigation is asked to call Detective McKenzie Kirlin at 302-576-3653, the Crime Stoppers tipline at 1-800-TIP-3333, or the Homicide Hotline at 302-576-3939.