Witnesses to the crash outside the Marriott Hotel in Trevelyan Square, Leeds, at about 3.10am today (Sunday) are also being urged to come forward.
West Yorkshire Police said the accident involved an Audi SQ5 and three people were thought to have witnessed it.
A police spokesperson said: "The incident occurred after the light blue Audi SQ5, registration DE6 EWS, was in collision with a 24-year-old woman while she was in the precinct area at the front of the hotel.
"The driver involved made off from the scene.
"The woman was taken to Leeds General Infirmary with a potentially serious head injury which is believed to be none life-threatening."
Sergeant Steve Suggitt added: “This was a serious incident in which a woman has been knocked down and sustained a head injury.
“Enquiries have been on-going to trace this vehicle and I want to appeal directly to the driver involved to come forward and make contact with us."
CCTV pictures of the car and potential witnesses have been released.
Sgt Suggitt said: “We believe the incident was witnessed by the group of people pictured and I would ask them to contact us as they may well have vitally important information about what took place.
“Those people, the Audi driver or anyone who has information about the car, or anyone who can assist the enquiry should contact the Eastern Area Roads Policing Unit on 101 referencing police log 250 of January 20.”