CCTV footage shows the smash and the moment two people ran away from the car which ploughed into the learner's vehicle.
The collision happened at the junction of Bridge Street and Camp Hill in Wordsley, near the Red House Glass Cone.
The incident happened at 6.15pm on Tuesday, with the incident captured on cameras at the nearby Ocean Boat fish and chip shop.
In the footage, a silver saloon car can be seen hitting a red car with a learner symbol, sending it spinning out, and ploughing into a low wall.
Two people are then shown jumping out of the badly-damaged silver car and running into nearby Bridge Street next to the Glass Cone.
A spokeswoman for West Midlands Police said the road was closed in the aftermath of the crash and that the driver who fled the scene had not been tracked down. No arrests have been made.
A spokeswoman for the West Midlands Ambulance Service said: "Two ambulances, two paramedic officers and a Critical Care Car from Midlands Air Ambulance attended the scene.
"Upon arrival we found a man who was the driver of the first car. He was assessed at the scene and had sustained injuries not believed to be serious. He received treatment on scene and was conveyed to Russells Hall Hospital for further assessment. No further patients require assessment."