More than 100 residents live in 67 flats the multi-storey Anderson Tower, but North Lanarkshire Council closed it yesterday while ScottishPower engineers replaced mains cables.
A council spokesman said: "Initial testing has shown a number of positive results within the building. As a precautionary measure, movement to and from the tower was restricted earlier today. While we do not believe there is any immediate risk to health, the wellbeing of our tenants is our priority."
Arrangements are being made to find alternative accommodation and the council aims to return people to their homes shortly.