It happened around 8:30 p.m. on the 500 block of East Westmoreland Street in the city's Kensington section.
Police say the 27-year-old woman was making a pre-paid delivery to a private residence when she was approached by two men who announced a robbery.
Police say the men ransacked the woman's car after they learned she didn't have any money. The suspects then tried to take the woman's fanny pack and a struggle ensued.
According to Chief Inspector Scott Small, the woman was grazed by a bullet during the attack.
"They began striking her in the head and face with their weapon. And then at least one shot was fired, striking her in the face. But she's grazed, so she's very lucky to have just a graze wound to her face," said Small.
The delivery driver was hospitalized and is expected to survive.
The suspects, who police say were wearing ski masks at the time of the attack, were able to get away.
One of the men is described as wearing a dark jacket and light or white-colored pants. The second suspect was wearing all dark clothing.
Anyone with any information is asked to call police at 215-686-TIPS.