The 87-year-old was struck by a vehicle, thought to be a blue BMW 1 series car, at around 7.40am in Hospital Street, Dundee.
The driver of the car did not stop and continued driving along Hospital Street towards Clepington Road.
The woman was taken to Ninewells Hospital in Dundee for treatment to head and hip injuries.
Police Scotland appealed for information about the incident.
The car had a registration number beginning ST59 and might have damage to its front or bonnet as a result of the collision.