Emergency services were called to the scene at Everard Drive at 2.50am today.
The body of an elderly woman was found within the property and investigations are now underway to determine the cause of the fire.
A Strathclyde Police spokeswoman said: "At 2.50am police received a report of a fire in Everard Drive, Glasgow.
"Emergency services attended and the body of an elderly female was found within the property.
"An investigation is underway to find the cause of the fire."