Emergency services are currently evacuating residents from the burning building in Kenmure Street.
Nine fire appliances have been called to tackle the blaze after crews were alerted to the fire at about 5pm today.
The public have been asked to avoid the area while emergency services deal with the incident.
No injuries have been reported so far.
A Scottish Fire and Rescue Service spokesman said: “We are currently in attendance at a large fire in Kenmure Street, Glasgow.
“Operations Control mobilised nine appliances including two height appliances after the alarm was raised at 4.53pm.
“We ask the public to avoid the area and allow access for emergency services.”
A police spokesman said: “We received a report of a fire at a property on Kenmure Street in Glasgow around 4.55pm on Wednesday, 1 April, 2020.
“At this time, officers are assisting the Fire Service with evacuating residents and implementing road closures in the area.”
A Glasgow City Council spokesman said: “Kenmure Street is currently closed between Maxwell Road and Melville Street due to a house fire.
“Drivers are advised to avoid the area.”