The 58-year-old woman was crossing Whitehall Road at around 6.40pm on Wednesday 23rd January in the direction of Marsland Road close to the junction with Brooklands Road when she was hit by a red car.
The car did not stop and so far has not been traced.
The woman was taken to Wythenshawe Hospital where she remains in a stable condition.
PC Paul Shore said: “The vehicle would have been damaged to the front or the near side front by the collision and so I am also urging vehicle repair workshops in the area that may have recently repaired a vehicle matching this description to also contact police.”
Anyone with information should call police on 101, or the independent charity Crimestoppers on 0800 555 111.