The local authority has the power to protect the public from any building which is determined to be an 'imminent danger'.
The building is located on East Clyde Street, which is currently closed between Maitland Street and Sinclair Street.
Diversions are in place.
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Angus Gilmour, Head of Planning and Regulatory Services, said: "We are taking immediate action to ensure public safety. We will take any action needed to keep people safe in and around dangerous buildings.
"We have now moved occupants safely from the building and, through our housing team, in consultation with registered social landlords, will arrange alternative accommodation.
"The road will remain closed to allow a structural survey to be commissioned to determine exactly what work is needed to bring the building back up to a safe, liveable standard."
Mr Gilmour added the council will ensure the property's owners will "fulfil their responsibilities to carry out the necessary repairs".
(LM)
