The pensioner was walking along the pavement in Millbrix Avenue, in the Knightswood area of the city, when she was struck at about 3.10pm on Saturday.
Emergency services attended but the woman died at the scene.
A 23-year-old man was arrested in connection with the incident and was released pending further inquiries.
Police are appealing for information about the incident, which they said involved a red Honda quad bike.
Sergeant Nikki Taylor, of Glasgow Road Policing Unit, called for anyone who was in the area at the time and “saw a quad bike being driven” to come forward.
“We know there was a white van in the street at the time of the incident and we would appeal to the driver to get in touch as they may have vital information,” the officer said.
“You may also have dash-cam or home CCTV that can help us, please look back. We urge you to get in touch.”
The road was closed for nearly five hours while police carried out investigations.
:: Anyone with information is asked to contact Police Scotland on 101, quoting incident number 2717 of Saturday July 13 2019, or contact Crimestoppers on 0800 555 111, where information can be given in confidence