The infected man was staying at the Novotel & Ibis Ellerslie MIQ facility, on Green Lane East, and absconded at approximately 12.50pm today.
The escapee was arrested by police and taken into custody at approximately 1.14pm.
In a statement, Joint Head of MIQ Brigadier Rose King said: "The individual is a COVID-19 positive community case who has been in MIQ since October 23".
"The fact that someone has absconded from one of our facilities is a disappointing and unacceptable breach. We are investigating how this happened," Kind said.
A police spokesperson said the 33-year-old is now in custody in the Auckland District Custody Unit in Mount Eden and charges are being considered.
"Police staff who interacted with the man today were wearing appropriate PPE," the police spokesperson said.
A police presence was seen blocking Mitchelson St, Ellerslie, a few blocks from the Novotel & Ibis Hotel on Green Lane East.