Police are investigating a report of three windows being damaged at the Happyhansel Primary School in Walls.
The incident is said to have happened between the evening of Monday 28th October and 9am the following morning.
The outside of the windows suffered scratches in the incident.
Meanwhile, police are also appealing for information regarding damage to a white Peugeot van which was parked on South Lochside in Lerwick.
That incident is said to have happened between 3pm on Saturday and 8.30am on Monday.
The van received dents to its nearside panel.