North Lanarkshire Council said more than 100 residents had been moved out of Anderson Tower in Motherwell as a precaution.
Scottish Power had been replacing mains cables in the building at the time.
A council spokesman told the BBC initial testing had shown “a number of positive results” but said there was not thought to be any immediate risk to health.
He said: “As a precautionary measure, movement to and from the tower was restricted earlier today.
“However, in light of the results, we have decided to decant our tenants.
“While we do not believe there is any immediate risk to health, the wellbeing of our tenants is our priority.”
Residents were moved to a temporary reception centre and offered alternative accommodation.
“We are hopeful residents will be able to return to the building as soon as possible,” the spokesman added.