The incident took place inside Murano Deli along the 6600 block of Castor Avenue around 7:40 p.m. Wednesday.
Police say two men became engaged in an argument and, at some point, either the owner or patron tried to intercede; both were stabbed.
One of the victims, described as the 35-year-old store owner, was stabbed in the chest.
The other victim was a 38-year-old customer who was cut to the hand.
Both were transported to Aria Health Torresdale Campus for care.
Police say the suspect attempted to flee on foot but was pursued by witnesses and apprehended by police.
There is no word yet on what the argument was about.
Officials say it is possible the incident was captured on surveillance video.
Police also say they also recovered the weapon.