Police shot the shark, believed to be 12-foot, an unknown number of times. It is not known whether any sharks have died.
Police believe the shark was likely to be a Great White.
Dr Malcolm Francis, a NIWA Principal Scientist who studies sharks, told One News that based on the reports it is likely the attack was by a Great White Shark.
He said there are few other species that grow to 12-foot long - believed to be the length of the Muriwai shark.
He said Great Whites are known in the area and it is likely the shark mistook the person swimming as a seal.
A press conference is to be held at the beach soon.