The predator was chasing a seal around the bay when the seal used the surfer as a decoy, and the shark bit the victim twice, it said.
The surfer, in his 50s, suffered non-life-threatening injuries, 9News reported.
A 29-year-old surfer survived an attack at the same beach in 2020, suffering leg injuries from a great white shark.
Bronze whaler sharks can get as large as 3m long, but usually average 1.5-2.5m in length according to NIWA.
They are one of the most abundant large shark species in New Zealand coastal waters.