The 17-year-old was talking to her mother after a shopping trip when she was struck in Bromsgrove Street, Birmingham.
West Midlands Police said it wanted to trace a dark-coloured BMW 5 Series following the incident at about 18:30 GMT on 28 January.
The victim remains in hospital with serious injuries.
PC Mark Nicholson, from the West Midlands Police traffic unit, said: "A teenager suffered serious neck and head injuries and is still in shock from what happened.
"I would urge anyone with information to call us and I want to appeal directly to the driver to do the right thing and come forward."
The footage shows the car emerging from a side street before mounting the pavement and running the girl down.
The driver sped off without stopping.
Footage has been released of the moment a teenage girl was hit by a car while walking along a pavement.