The collision, which involved a grey VW Tiguan car, happened on Elmbank Street at its junction with St Vincent Street in Glasgow at around 8.15pm on Thursday.
The pedestrian, a woman aged between 50-60 years old, was taken to the city’s Queen Elizabeth University Hospital, where medical staff describe her condition as critical.
The driver of the car, a 57-year-old man, was not injured.
Police are appealing for information as they try to establish the woman’s identity.
Sergeant James Crawford, of the road policing unit in Glasgow, said: “It is imperative we find out who this woman is so we can contact her family and let them know what has happened.
“She is aged between 50-60 years old, has shoulder length brown hair which was tied back and she was wearing a long cream-coloured jacket with a large fur hood.
“She was also wearing blue jeans and brown boots.
“She walked with a clear limp to her left leg and we believe she may be from the local area.
“I am appealing to anyone who was in the area at the time of the crash to contact officers with any information they may have which could assist our investigation, or who can help us identify the woman involved.”
Anyone with information is asked to call Police Scotland via 101, quoting incident number 3467 of February 2 2023.