Police have launched an investigation into how the 86-year-old sustained her injuries.
The woman collapsed at around 5.10pm on Monday, as she was crossing Mossvale Road, in Craigend.
She was rushed to Glasgow Royal Infirmary and staff describe her condition as "critical".
Constable Hugh Nicholls, said: "At this time we are not sure whether the woman was struck by a car, which stopped at the scene, took unwell, collapsed or tripped and fell.
"A number of people went to her aid."