It will come into effect at 17:00 local time on Thursday (07:00 GMT).
The lockdown was called for the whole of the Australian Capital Territory - home to around 400,000 people - because authorities do not know how the infected person caught the virus.
Residents will only be able to leave home for essential reasons.
Queues were reported at supermarkets as the lockdown approached.
Australia is struggling to get on top of the highly infectious Delta strain, which has resulted in two of its largest cities - Sydney and Melbourne - going into strict lockdowns.