The accident happened on Barrhead Road at the rear of the massive Silverburn Shopping Centre in Pollok.
Carol Collins, 68, and a 67-year-old woman were both injured in the accident which happened at about 4.45pm on Saturday.
They were taken by ambulance to the Southern General Hospital, where Ms Collins died a short time later.
The other woman suffered injuries to her arm and is being treated in hospital.
Relatives of both women have been notified of the accident.
The 42-year-old male driver of the black Range Rover, who was uninjured, stopped at the scene.
Police closed busy Barrhead Road for almost six hours while officers examined the area. Floral tributes have been attached to railings at the pedestrian crossing where the tragedy happened.
One has a message attached which reads: "RIP Carol. We will all miss you. Kenny."
Constable Paul McNamee, of the road policing unit, said: "There were a number of people in the area when the accident happened.
"We have managed to speak to some of them, however would still appeal for further witnesses to come forward."
Anyone with information is asked to contact the 101 non emergency number. Police said Ms Collins lived in the Pollok area.
Earlier, Maryhill Road in Glasgow was closed in both directions between Bilsland Drive and Ruchill Street as a result of a "police incident". The road was closed just before midnight on Friday and reopened at around 4am on Saturday.