At 8.20pm Sunday, police were called to a Hassall Street fast food restaurant.
Police have been told a car hit the mother and her two children at low speed as they walked through the car park.
The 37-year-old woman and a three-year-old did not appear to be injured; however a seven-year-old girl suffered serious leg and head injuries.
Emergency services attended and she was taken by ambulance to Westmead Children’s Hospital and is in a critical but stable condition.
Police established a crime scene and inquiries into the incident are continuing.