A white Mitsubishi flatbed truck crashed through the gates of West Launceston Primary School about 10pm on Sunday night.
The single-vehicle crash caused considerable damage to the gates, garden and seating areas at the front of the Denison Road school.
The truck driver left the scene of the crash before police arrived.
A witness told police a man and a woman were seen walking away from the crash.
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Investigations are ongoing.
Anyone with information about the crash or who saw someone acting suspicious in the area is asked to call police on 131 444 and reference OR 623273.
Alternatively, anonymous reports can be made to Crime Stoppers on 1800 333 000.