The collision happened at the crossing outside Lloyds TSB bank in Church Street at about 11.15am on Tuesday.
The pedestrian, a 15-year-old girl, was on the crossing when she was knocked to the ground by a newer-shape silver Vauxhall Corsa, driven by a woman with blonde hair, who appeared to be in her late teens or early 20s.
The driver failed to stop and continued on towards Oswestry. Police are checking CCTV images from the area in an attempt to identify the vehicle.
Police Constable Andrew Marston, who is investigating the incident, urged the driver of the car to come forward before the police came to her.
“Fortunately, the teenager was not seriously hurt but left extremely shaken and the woman driving the car did not stop after the collision but continued towards Oswestry,†she said.
“I would urge her to contact police on 0300 333 3000 or visit her nearest police station as a matter of urgency.
“We are examining CCTV as part of the enquiry in an attempt to identify the vehicle and driver involved.
“We do believe that she was aware she had collided with the girl and it is important that she contacts police, as failing to stop following a road traffic collision is an offence.
“If anyone saw the collision take place but has not yet spoken to police, could they also get in touch as soon as possible.â€