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The man was reported missing at 11pm yesterday for half an hour from the Sudima Rotorua facility, sparking a search by New Zealand Defence Force staff.
Police are investigating the incident and checking CCTV security footage to establish exactly where he went during that time.
"However, indications are that he did not move beyond the immediate area," a statement said.
It appears the man escaped through a fenced area.
"There is no information to suggest the man came into contact with any other person while he was outside the facility," authorities said.
The man involved was taken to hospital for assessment, due to concerns for his wellbeing.
The head of Managed Isolation and Quarantine, Air Commodore Darryn Webb, said there was a low risk to public health.
The man had tested negative for his day 3 test after arriving from Brisbane on September 8.
He remained symptom-free and was now in his ninth day of isolation, Webb said.
"I would like to reassure people - particularly those in Rotorua who have concerns - that the health risk as a result of this incident has been assessed as low."
Security had now been "bolstered" at the site as a result of last night's incident, he said.