At one point, the fire was so fierce, Scottish Fire and Rescue had committed six appliances to fight the blaze, but it was to no effect and the building could not be saved from destruction.
The fire was reported to emergency services at around 7am with both fire services and police attending the scene.
Local officers at the scene said there had been no casualties reported, and the Scottish Ambulance Service said they were not needed at this incident.
"Emergency services remain in the area and enquiries to establish the cause of the fire will be carried out. There have been no injuries reported.”
A Scottish Fire and Rescue Service spokesperson said: “We were alerted at 7.14am on Friday, 25 November to reports of a building fire in Claremont Gardens, Milngavie.
“Operations Control mobilised a total of six fire appliances and crews remain in attendance.
"There are no reported casualties."