Emergency services scrambled to Carlton Place, near the River Clyde, in the Gorbals area after the alarm was raised at around 8pm on Monday.
Images shared with Glasgow Live showed flames tearing through the roof and windows of the building as firefighters surrounded the area.
Labour MSP Paul Sweeney posted on X, formally Twitter, saying: "Another fire at the historic Carlton Place terrace. This one is more severe and has taken hold in a section of the roof. Thankfully, the firefighters have contained the fire in the attic space and are bringing it under control. We need urgent Council intervention to save it now."
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