The damage was caused to the flooring within the Pirate Ship at Saumarez Park.
The damage was such that the area is now unsafe for children to continue playing there, so the Pirate Ship has had to be sectioned off until it is repaired.
A spokesman for police said: “It is unacceptable and is causing inconvenience for children and families who would otherwise enjoy the playground.”
Anyone who either witnessed anything over the weekend, which is when the damage is believed to have been caused, is urged to contact PC 152 Taylor on 725111.
Alternatively, anyone with information can anonymously contact Crimestoppers on 0800 555 111.