Anyone arriving in New Zealand must spend at least 14 days in managed isolation or quarantine.
The 10,000th passenger entered the facilities at the weekend on a flight from Melbourne.
At any one time, more than 2000 people are in hotels being used for isolation or quarantine in Auckland.
So far about 8000 people have completed their stay in Auckland or Christchurch and have returned home.
Bloomfield said protecting the border was a "critical" part of the Government's strategy to eliminate Covid-19, especially now that domestic cases are at such low levels.