Tasmania Police responded to a unit fire at unit 32, 8 Merrys Lane, South Launceston about 7.20pm on Sunday night.
According to police, the fire was first observed when an occupant of a nearby unit noticed smoke from the vacant residence.
Three Tasmania Fire Service crews extinguished the fire - the unit was completely destroyed.
The fire caused damage to adjacent units which were unoccupied at the time of the incident.
Tasmania Police has said the circumstances surrounding the fire are suspicious - a fire scene examination is being undertaken to determine the cause of the blaze.
Police are asking for any witnesses or information regarding the fire to assist in investigations.
Information can be provided anonymously to Crime Stoppers on 1800 333 000.