Police are appealing for witnesses following the collision in Beechdale Road in Beechdale shortly before 12.30am on 21 July.
The 18-year-old rider suffered a fractured skill and injuries to his leg and ankle.
He spent two days in hospital and is now recovering at home.
The collision involved a Volkswagen Golf and police are appealing for help in finding the person who was driving it.
The suspect is described as a man, aged 20-30, medium build and just under 6ft tall.
PC Matthew Hempsall said: “This was a serious incident and it was sheer luck that the victim was not fatally injured.
“The driver fled the scene and we are now carrying out a range of enquiries to identify the driver and would ask that person – or anybody who knows them – to come forward.
“A number of drivers were in the area at the time so we would also ask anyone with dashcam footage or who saw what happened to contact us.
“We will continue to use every tactic at our disposal in order to protect all our road users and will take swift and robust action against anybody who endangers the lives of others.”
Anyone with information is asked to contact police on 101 quoting incident number 23 of 21 July. Alternatively, you can pass on information to independent charity Crimestoppers anonymously on 0800 555 111.