"The public health unit in Napier and other port authorities there will work carefully and closely to get in place plans to isolate and test the crew there ... no one on board is symptomatic at this time," Bloomfield said.
He said the case had been caught early and the risk of onward transmission had been quickly contained.
A Hawke's Bay DHB spokeswoman said the DHB was working closely with the Ministry of Health and the ship remained offshore this afternoon.
A Napier Port spokesperson said the port was notified this morning that the vessel was heading to Napier.
"The vessel is at anchor, it is not coming into Napier Port.
"We will facilitate the public health unit to get medical staff onboard if required and will follow any border directive we receive from the Ministry of Health."