The parasite does not pose any food safety risk but can kill flat oysters, putting the entire Bluff oyster trade at risk.
The Ministry for Primary Industries has now commissioned scientists at Niwa to test about 2200 oysters across 15 sites on the Strait to better understand the extent of the recent threat.
Niwa biosecurity scientist Anjali Pande said that in all the cases overseas, wild and farmed oyster populations that became infected effectively died and had not really recovered.
"Overseas it has caused catastrophic decline so now we kind of watch and see because it's the first time this particular parasite has been found in this particular oyster species in this particular environment.... so we don't 100 per cent know, all we have to go on is what's happened overseas."
Bonamia ostreae was first found in New Zealand in the Marlborough Sounds six years ago and then in 2017 from oysters in Big Glory Bay on Rakiura - Stewart Island.
The detection in Rakiura prompted the Ministry for Primary Industries to destroy oyster farms there, as well as farms in the Marlborough Sounds.
The recent Foveaux Strait detection is the first time the parasite has been found in the wild fishery in New Zealand.
MPI biosecurity manager Catherine Duthie said the results from Niwa's testing would inform the next steps in its response. A technical advisory group was also being established, she said.
"As we've seen from overseas, this is a disease that can significantly affect oysters, so we need to be very careful about any decisions that we do make."
Eradication was not an option that was being explored, because of the wild marine environment the biosecurity response was centred on, she said.
Niwa fisheries scientist Keith Michael said the Bluff oyster trade generated about $30 million of revenue annually and was a unique fishery.
"It occurs in very deep water, strong currents. Foveaux Strait's exposed to high storm surges which means there's tremendous swells that move a lot of sediment.
"Oyster fisheries overseas are based in estuaries and shallow embayments, so they're ... relatively muddy, [so] the environment and habitat for oysters in Foveaux Strait is very, very different."
He said the parasite had the potential to cause significant economic, cultural and ecological losses.
"Oysters are often foundation species... they provide the settlement substrata for other organisms to settle and grow and to bind together and create some of the diverse habitat that is important for juvenile fish and general community function."
MPI said some initial results from Niwa's testing were expected next week, with the final findings due around mid-June. It said public meetings with local iwi, fishers and other stakeholders were being planned.