More than 20 firefighters attended the scene in Greenhead Street, near Glasgow Green, when flames were first spotted shortly before 9.30pm on Monday.
Fire chiefs said residents living in a nearby five-storey tenement were evacuated from their homes as a precaution.
Investigators said the fire, which broke out at the former Inn on the Green, was “deliberately set”.
A Scottish Fire and Rescue spokesman said: “Crews were faced with a well-developed fire in the roof of the disused, four storey property.
“However, the main concern was for the adjoining five storey block of flats, which were all occupied.”
Crews worked through the night to bring the blaze under control and remained at the scene until shortly after 3am on Tuesday.