Damage at the grounds was caused by a vehicle doing skids last Sunday.
Inquiries led police to the vehicle and a 17-year-old male, who will now go through a youth justice process.
Constable Derek Dudley, of Te Anau, said in a statement the incident was extremely disappointing and caused senseless damage in the community.
"A lot of money, time and effort go into the upkeep of these grounds, and they should be for everyone to enjoy," he said.
"We won’t tolerate this kind of reckless behaviour and we are glad to have arrested someone so they can be held account."