A fence post was deliberately set on fire at Sound Primary School in Lerwick in the early hours of Sunday, the police say.
The police would like to speak to witnesses about the incident, which happened about 4am and was described as “wilful fire-raising”.
The fire, which was put out by the fire brigade, resulted in damage to the post. The police say they are keen to speak to a group of youths who were seen running away from the area at the time of the incident.
Anyone with information is asked to contact Police Scotland in Shetland on 101, Crimestoppers anonymously on 0800 555 111 or alternatively attend at the Lerwick station.