The fire service was called to a blaze on the fourth-floor landing of the Pomarium Flats in Pomarium Street, Perth, at about 12pm. No one was injured.
Energy company SSE advised that the electricity supply to the block of flats be turned off as a precaution while the cause of the fire is investigated, police said.
As a result around 20 people will be moved to alternative accommodation until the supply is reconnected.
The housing team at Perth and Kinross Council is at the scene helping to re-house residents.
Anyone with information about the fire is asked to call Police Scotland on 101 or Crimestoppers on 0800 555 111.