The incident happened at Whitesands around 8:15pm on Wednesday.
The 45-year-old was taken to Dumfries and Galloway Royal Infirmary where she later died.
She has now been named by Police Scotland as Nicola Kirk.
A 26-year-old woman was also struck by the car, but did not sustain any serious injuries.
Detective Inspector Dean Little said: “Our thoughts are with the woman’s family and friends at this extremely difficult time.
A 35-year-old man has been arrested and charged in connection with the incident.
He is due to appear at Dumfries Sheriff Court.