The incident happened shortly after 3:00 a.m. Sunday at 48th Street and Osage Avenue.
Police say officers discovered the woman unconscious on the street. She has been identified as 23-year-old Morgan Jones, a student at Temple University.
She was rushed in critical condition to the Hospital of the University of Pennsylvania with head injuries and broken bones.
Because of the time of the morning, many residents say they didn't hear or see anything until police and paramedics arrived.
"I'm a little surprised because it's really nice around here. It's a shame, it just shows how low some humans can be," said neighborhood resident Charles McNeil. Surveillance cameras at a nearby apartment building captured the hit-an-run. In the video, the victim can be seen dangling from the side of the taxi before she fell to the ground.
On Monday afternoon, police said they had located a vehicle that may be the cab involved, but were not yet sure. The were able to question the driver. He has not been charged.
Police were contacting the Philadelphia Parking Authority, who keeps track of all the taxi locations. The hope is to see who was working that night, who was in the area, and then confirm who was actually behind the wheel of the striking vehicle.
Anyone with information is asked to contact Philadelphia Police at 215-686-TIPS (8477), text a tip to PPD TIP (773847) or through PhillyPolice.com.