The man was tested onboard when the ship arrived at the East Arm wharf on Sunday night.

He has since been admitted to the Royal Darwin Hospital, where he is in isolation.

The majority of other crew members have been transported to a separate section of the Howard Springs quarantine facility.

They will complete 14 days of mandatory supervised isolation unless the Diamantina's operators elect to leave Darwin sooner, in which case they will be escorted back to the ship.

Some crew members are required to remain on board the Diamantina to comply with international maritime law. Testing will be undertaken and they are required to stay on board in self-isolation.

Those who came into contact with the ship will also be placed into isolation. However, they were wearing personal protective equipment when boarding the vessel and did not contact the infected man.

Northern Territory Health Minister Natasha Fyles said there was no indication anyone had breached the territory's public health orders.

"We've certainly had very strong compliance to date and authorities have been appropriately engaged, whether it's from Health, Maritime Safety or from police," Ms Fyles told reporters on Tuesday.

"These vessels, not only do they bring goods that Australians need ... these are vital supply chain vessels."

The man's case takes the total number of coronavirus infections diagnosed in the NT to 75.

All have been related to international or interstate travel, with no cases of community transmission.

Australian Associated Press