North Lanarkshire Council moved all tenants from Anderson Tower in Motherwell after concerns were raised on Thursday.
The substance is thought to have been disturbed during cabling work carried out by ScottishPower.
The council said it ensured all tenants were accommodated overnight in hotels, temporary council accommodation or with friends and family.
Some asbestos dust has been found in halls and lobbies, with clean-up work starting on Thursday and continuing to Monday. Residents are unable to return until then.
The council's housing operations manager, Stephen Llewelyn, said: "Tests have shown small amounts of asbestos dust in hall and hall cupboards as well as lift lobbies.
"As a precautionary measure the contractor has been instructed to clean all halls and communal areas.
"Tenants will not be able to return to the building until we are satisfied that this is complete."
"We are working closely with ScottishPower, their contractors and the Health and Safety Executive to ensure all safety standards are met."