North Lanarkshire Council said it decided to "decant" tenants from Anderson Tower in Motherwell as a precautionary measure after air quality testing today.
The substance is thought to have been disturbed during mains cabling replacement work which was being carried out at the tower by Scottish Power.
The council is closing the block to allow further investigation and arranging other accommodation for tenants.
A spokesman for North Lanarkshire Council 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.
"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 well-being of our tenants is our priority.
"A temporary reception centre has been identified and we are arranging alternative accommodation.
"We are hopeful residents will be able to return to the building as soon as possible."
The multi-storey block houses more than 100 residents in 67 flats.