The Scottish Fire and Rescue Service said crews were met with a "well-developed fire" when they went to the scene in High Street after the alarm was raised at 1.27am on Tuesday.
Police have appealed for any witnesses after the flames seriously damaged the run-down premises above the Old College Bar
Nine fire appliances and around 40 firefighters were used to bring the blaze under control. Firefighters remained on the scene as of 4pm on Tuesday monitoring for any hotspots.
There were no reports of any injuries.
Detective Constable Neil Bonsor said: "Our enquiries are ongoing into the circumstances surrounding the incident.
"The blaze has caused significant damage to the building's structure.
"We would urge anyone who was in the area around the time of the incident and who saw any suspicious behaviour to contact us."
Anyone with information should call Police Scotland on 101, quoting incident number 0119 of May 4 or call Crimestoppers anonymously on 0800 555 111.
Roads in the area, including parts of High Street, Duke Street and West George Street, were closed while emergency services dealt with the incident.
The blaze also temporarily affected train services to High Street, with passengers asked to travel to and from Glasgow Queen Street Low Level on Tuesday morning.
Sources say the Old College Bar, which is reputedly among the oldest pubs in Glasgow, appears to be undamaged following the fire. However, the premises will likely have suffered water ingress from hoses being used on nearby buildings.
Services to High Street later resumed.