She was hit by a black Range Rover Evoke on Gartocher Road, in Sandyhills, at about 14:00 on Thursday.
The woman is being treated at Glasgow Royal Infirmary where her condition is described as serious but stable.
Sgt Nicola Taylor said that a number of people came to the woman's assistance but officers still needed to speak to anyone who witnessed the crash.
A 78-year-old woman has been seriously injured after being struck by a car while crossing a road in Glasgow.