Dentist Monica Taylor was killed last Friday in the blaze at the family home in Islay Drive.
Police and the fire service were called around 12 noon to the home Monica shared with her husband George and their children, Andrew, Sarah and Matthew.
A friend of the family, who did not wish to be identified said of Monica: “She was the perfect mother and a great person”.
The tragedy has left everyone who knew Monica in shock.
The family friend said: “No one can believe what has happened. It’s the worst kind of tragedy imaginable.
“Our hearts just go out to Monica’s children, her husband and everyone who knew and loved her. It’s unbelievable.
“Everyone is just stricken with grief.”
Monica and George, who were both dentists, were believed to have worked together until recently at a practice in Mount Florida.
A resident in Islay Drive said: “Everyone is in shock. It’s a very quiet street.
“There have been police officers and loads of firefighters here since early in the afternoon. I’ve been here for years and I have never seen so much activity. The house has been cordoned off and the police have said they aren’t able to give us any information.
“We had heard someone died. It’s just awful. I had seen the family around – they seemed very nice.
“It really is just absolutely heartbreaking for everyone concerned.”
Police Scotland said: “At around 1pm on Friday, police were called to a report of a fire in an outhouse at a property in Islay Drive, Newton Mearns.
“Emergency services attended and a body was discovered in the outhouse.”
A post mortem will be carried out. Inquiries are continuing and a report will go to the fiscal.
The Scottish Fire and Rescue Service said: “One appliance from Clarkston and one from Pollock attended reports of an outbuilding on fire. Crews used two hose reel jets to extinguish the fire.”