The individual was self-isolating at the time they tested positive and is reportedly at home continuing their self-isolation.
Public Health and the States are working with Alderney's health service and government to ensure they are fully supported.
With contact tracing already having taken place, Public Health are confident that there are no further contacts of this case outside of their household, meaning there is very low risk of further spread of the virus in the northern isle.
Like the rest of the Bailiwick, Alderney has been in lockdown since 23 January, with all islanders only allowed out for their two hours of exercise or essential reasons.
Face coverings are also strongly recommended when leaving the house.
More than 700 elderly and at-risk Alderney residents have received their first dose of the vaccine.
Director of Public Health Dr Nicola Brink recognised this would be worrying news for Alderney residents, but sought to reassure the community.
'Because we identified this person early as a potential contact, they have been self-isolating for several days. Coupled with how Alderney is already in lockdown, we have been able to complete our contact tracing assessment very quickly and confirmed there are no further contacts outside of the household.'
But this was not a reason to be complacent and anyone who develops even mild symptoms should still report them immediately.
'We have worked closely with the team at the Island Medical Centre from the start of the pandemic and they will ensure that the person concerned will receive the appropriate clinical care, if they need it,' she added.
President of the States of Alderney William Tate said the strict following of lockdown rules by the community had put the island in a good place as the first positive case came to light.
'I’m extremely reassured by the encouraging outcome of the contact tracing work carried out overnight.
'All I ask of Alderney residents is to keep doing what you’re doing, follow the lockdown rules, go out as little as you can and keep your distance and wear a face covering when you are out,' he said.
Alderney residents need to continue following the lockdown rules, but there is no need for them to do anything differently as a result of this case. Anyone who develops any symptoms however mild, should phone the clinical helpline on 756938 or 756969, or phone their GP.