Six fire engines fought to bring the blaze under control which broke out at around 10pm at the Gartshore Estate at Waterside Road.
It is believed the stable buildings which have been derelict for some time, were gutted.
As the Herald went to press on Monday, the fire service were investigating to establish if the blaze had been started deliberately.
Waterside Road was closed overnight on Saturday and for part of Sunday between Drumgrew Bridge and Langmuir Road as a result of the incident.
One eyewitness said: “The whole place was in flames.”
Others spoke of their shock on social media. One posted: “How sad. A lovely old stable block. Such a waste.”
A Scottish Fire and Rescue Service spokesperson told the Herald on Monday: “We were alerted at 9.51pm on Saturday, January 15, to reports of a fire affecting a building in Waterside Road, Kirkintilloch.
“Operations control immediately mobilised six fire engines to the location and firefighters extinguished the fire. Crews left the scene after ensuring the area was made safe.”
Gartshore Estate was bought in 1870 by Alexander Whitelaw and his son built a new house in about 1887. Throughout the late-19th century and into the 1930s the Whitelaw family created an estate landscape with gardens, parkland, extensive woodland and estate buildings. The original 17th century house on the estate was demolished in the 1950s but the stables remained.