The incident happened after midnight inside the hospital located on North Broad Street in the city's Olney section.
Police say two male workers, a 46 year old and a 56 year old, got into an argument that ended when the older man stabbed the younger.
The victim suffered wounds to the hand, chest and shoulder after being stabbed four times.
He was rushed to the emergency room inside the hospital for treatment and is listed in good condition.
The attacker fled the hospital on foot.
Einstein security personnel and Philadelphia police officers gave chase and apprehended the suspect near the Broad and Olney SEPTA station.
The names of the men have not been released.
The hospital issued a statement, saying the attack "was an isolated incident that occurred in a non-patient care area. At no time were patients at risk. The suspect is in police custody...."