Member of armed forces becomes first confirmed case on Falkland Islands
Brigadier Nick Sawyer, Commander of British Forces South Atlantic Islands (BFSAI), said the patient, who has not been named, is in a stable condition in the remote archipelago's hospital.
They became unwell at Mount Pleasant Complex, a Royal Air Force base on the British territory.
Brigadier Sawyer said: "The individual followed all the correct processes and self-isolated when they started to show symptoms. They were closely monitored and after a deterioration in their condition the individual was transferred to KMH (King Edward VII Memorial Hospital).
"Mount Pleasant Complex and Ascension Island continue to implement the same strict isolation and social distancing measures as the UK and these are also aligned with the Falkland Islands Government direction.
"This is a timely reminder that we must all continue to be self-disciplined with our personal health procedures and observe social distancing."
The Falkland Islands Government said in a statement that the patient is not on a ventilator.
Six British Army medics have been deployed to the Falkland Islands this week to give support during the coronavirus pandemic.
Additional supplies of oxygen, medicine and personal protective equipment have also been sent to the islands.
The islands' chief medical officer Dr Rebecca Edwards said: "We knew the day would come when we would have our first confirmed case, and in some respects we are fortunate that we have been Covid-19-free until now as we have taken this time to plan our approach within the hospital and also from a wider perspective.
"We have reorganised the hospital and staffing arrangements, and put our supplies and pharmaceuticals in place, which many countries were not in a position to do before they identified their first cases."
Ms Edwards acknowledged that residents on the islands will be "concerned about this development" but insisted that the King Edward VII Memorial Hospital has been undertaking "strict isolation procedures for patients with infection".
She added: "We are working with BFSAI on tracing people who may have come into contact with the individual. This is an effective way to identify people who may have been in contact, so suitable next steps can be taken."