Officers found no-one on the island.
Fire and Emergency New Zealand shift manager Blair Walklin said access to the island was a bit of a "logistical nightmare", but they were working with authorities to determine the cause and spread of the blaze.
By about 4pm, the fire had razed about 1ha of pine and scrub forest.
Crews had been able to dampen down most of the fire by then, Mr Walklin said.
He said Fenz was grateful for the support of Warrington surf lifesavers, who helped officers get to the island.