Rest centres are being set up for residents and a city council meeting is postponed.
The council said it had been carrying out building surveys on Barton House, the oldest in its estate, as it decided on the long-term future of the block.
During the surveys, experts discovered that the building's structure could be "compromised" in the event of a fire, explosion or large impact.
Further surveys are planned but in the meantime, the authority said it was going door-to-door telling residents to leave. Declaring a major incident allows the council, which has said the issue is not related to RAAC concrete, to seek help from outside organisations.