It happened at the Parkcrest Village Apartments on Route 32 at around 7:00 p.m.
Police say 29-year-old Patrick Hastings was shot in the neck during what residents of the complex described as a struggle.
Hastings was airlifted to Cooper University Medical Center in Camden where he remains hospitalized following surgery.
Officers are reviewing video recordings and canvassing the area of the apartment complex.
Anyone with information about the incident is asked to contact Glassboro Det. Lou Butler at (856) 881-1501 or GCPO Det. Ron Koller at (609) 929-6348. Anonymous text messages can be sent to: GLOTIP & your message followed by CRIMES (274637).