Fire crews were called to the blaze in Sumburgh Street, Riddrie, as reported in late editions of yesterday's Evening Times.
The alarm was raised at around 6am yesterday, after the fire broke out at the complex managed by Blackwood Homes.
Strathclyde Fire and Rescue said the blaze started in the ground floor kitchen area.
After searching the property, firefighters discovered the woman's body.
A joint investigation between Strathclyde Fire & Rescue and Strathclyde Police was continuing today.
A Strathclyde Police spokeswoman said: "Emergency services were called to a report of a fire at a house in Sumburgh Street in Riddrie. The fire was extinguished and the body of a woman was found within.
"Inquiries are ongoing to establish the woman's identity."
It is not yet clear what caused the blaze.
A spokeswoman for Blackwood Homes said: "Blackwood is deeply saddened at the news that one of our tenants has died in a fire at their home.
"Our thoughts are with the tenant's family at this very sad time."
Fire officers stressed the importance of fitting smoke alarms.
One said: "It is absolutely vital that every home has a working smoke alarm."