The 52-year-old woman was found injured on Peat Road, in the southwest of the city, after being hit by a vehicle on Wednesday at about 7.20pm.
She has been taken to Queen Elizabeth Hospital to be treated for her injuries.
Officers have called for witnesses to come forward and said enquiries into the crash are ongoing.
A police spokesman said: "We were made aware around 7.20pm on Wednesday, 10 March of a 52-year-old woman found injured on Peat Road in Glasgow having been struck by a vehicle.
"She has been taken to the Queen Elizabeth University Hospital for treatment to serious injuries and enquiries are ongoing.
"The driver of the vehicle was uninjured.
"Anyone who witnessed the incident can call 101, quoting incident 2918 of 10 March."