The block of 15 flats is being redeveloped and the two residents of the only occupied flat were out at the time of the fire.
There were no casualties and no one had to be rescued.
Six fire crews from Eastleigh, St Mary's, Redbridge and Hightown attended the incident at around 7.20pm.
A witness has reported seeing two youths running from the building towards the Lakeside Estate at 7.30pm. They are described as white, slim and 5ft 8ins. One wore a woollen baseball cap and the other a beanie.
Anyone with information is asked to contact Detective Constable Claire Reynolds at Eastleigh on 101.
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