Fire crews were called to the incident around 5.35pm on Sunday at Charles Street in Springburn.
The blaze spread over a number of floors in the building, with smoke bellowing across a wide area.
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Fire engines from Springburn and Cowcaddens attended the multi-storey block.
A police spokesman said the fire was extinguished shortly before 9pm.
He added: “All persons that resided on floors affected have been evacuated and the local authority is assisting in providing a temporary rest centre for the occupiers.
“No one has been injured as a result of this incident.”
He added that the cause of the fire was unknown and a full investigation would be carried out by the fire service.