A total of 50 firefighters and eight fire engines attended the incident in Rathlin Street on Wednesday.
Though the fire is not being treated as suspicious, investigators are still trying to establish why the blaze started in the tenement roof.
The incident saw people in the block, as well as neighbouring properties, evacuated as fire bosses feared flames could spread to adjoining buildings
Group Commander Paul Nelis, of Strathclyde Fire & Rescue, said: "The roof is slightly damaged with a lot of loose tiles and, due to the fear of these blowing off, it was felt it would be unsafe to let residents use the closes.
"There was only one casualty; a male was taken to hospital with slight smoke inhalation."
The man was treated by paramedics and taken to nearby Southern General Hospital.
Fire crews were called out at around 4.40pm and their battle to extinguish the blaze continued until almost 10pm.
Crews remained at the site until around 11am yesterday.
Residents from neighbouring blocks have since been allowed back home but the those in the most badly affected tenement, No14, will stay in temporary accommodation until Monday at the earliest.