The victim is identified as Jamal Dean of Upper Darby, Delaware County.
Police say the 24-year-old was found lying in the fifth-floor hallway of the Henry on the Park apartments on the 7900 block of Henry Avenue around 10:30 p.m. Monday.
Dean had been shot multiple times in the chest, back, thigh and buttocks.
Medics pronounced him dead on the scene.
Police found 15 spent shell casings in the hallway.
Witnesses told police the victim does not live in the apartment complex, but was visiting family members and an ex-girlfriend.
The suspect fled the scene, but witnesses told police they know the identity of the shooter.
No one else was hit by gunfire.
"At the time, we know there were two other males, two females and a very young child, one year of age, that this dispute involved, but no one else was struck by gunfire," said Philadelphia Police Chief Inspector Scott Small.
Police believe the motive of the shooting was domestic in nature.
No arrests have been made.