At around 9.30am on 12th July, it is reported that the woman was walking in the car park area of the Co-operative supermarket in Rotherham Road, Dinnington.
It is believed that the elderly woman has been in collision with a vehicle in the car park area.
The woman is currently in hospital in a serious condition.
Officers would like to hear from anyone who may have been at the supermarket or using the cash machine in the car park area this morning, who may have witnessed the collision.
Call 101 quoting incident number 403.