Health authorities were advised early on Saturday morning a detainee at the Alexander Maconochie Centre had tested positive for COVID-19.

The patient, who will be included in the numbers announced on Sunday, had been transferred into the prison, ACT Chief Health Officer Dr Kerryn Coleman said on Saturday.

Investigations into what contact the person had with others are underway, she said.

"It's a vulnerable community and a high risk setting so ... we have some really good operational plans in place," she said.

"So this morning, that is exactly what we're working through."

The territory's health authorities are working to avoid an outbreak in the prison, like those seen in NSW.

Outbreaks have taken root in several correctional facilities across the state, with 175 cases linked to Sydney's Parklea prison alone.

Another 15 cases acquired in Canberra were announced on Saturday, as the territory passed another COVID-19 vaccination milestone.

More than 75 per cent of the population has received at least one dose.

On Friday the ACT became the first Australian jurisdiction to fully vaccinate half its population aged 16 and over.

Chief Minister Andrew Barr on Saturday said the race towards 80 per cent - the trigger for dropping most restrictions - will accelerate, with extra doses of Pfizer from the UK due to arrive soon.

Australian Associated Press