The Scottish Fire and Rescue Service said it received a call at 9.55am on Sunday about a blaze in building on Kingston Street.
There are no reports of any injuries and six appliances are currently on the scene to extinguish the flames.
Images and footage shared on social media shows huge clouds of smoke in the area.
Nearby residents were evacuated from their homes, according to the BBC and police have advised people to close windows.
A spokesperson for the Scottish Fire and Rescue service said: “We received a call at 9.55am this morning to reports of a building fire.
“There are four appliances in attendance. The fire is ongoing.”
Police are assisting the fire service, with road closures in place and drivers urged to avoid the area.
Glasgow City Council has closed off roads including part of Paisley Road West and Nelson Street, warning drivers to expect changes throughout the day.
Inspector Pauline Thomson said: “We are asking everyone to avoid the area while our colleagues in the Scottish Fire and Rescue Service deal with the incident.
“We are also advising people to keep their windows closed due to the smoke and not to gather on the street.”