The marine tested positive for the virus while in quarantine after arriving in Darwin on a charter flight and is being transferred to Royal Darwin Hospital.
NT Health Minister Natasha Fyles said the marine arrived in the Northern Territory "a few days ago" and disembarked through the military side of Darwin Airport.
Ms Fyles said the marine has potentially had "very, very minimal contact" with any Territorians.
The marine was in Darwin as part of the annual Marine Rotational Force hosted in the Northern Territory.
The original rotation of about 2,500 marines was postponed in March due to the coronavirus pandemic.
Defence Minister Linda Reynolds gave approval for the reduced contingent in May.