Police said the damage was caused by a vehicle doing skids on Sunday.
The 17-year-old culprit would go through a youth justice process
Constable Derek Dudley, of Te Anau police, says it was "extremely disappointing seeing this kind of senseless damage".
“A lot of money, time and effort go into the upkeep of these grounds, and they should be for everyone to enjoy.
“We won’t tolerate this kind of reckless behaviour and we are glad to have arrested someone so they can be held account.”