In a separate statement, Air NZ said the temporary hold will be in place for the next three weeks.
The need to align daily arrivals with capacity at the facilities "may mean some customers will need to be moved to another flight," it said.
Outbound services from NZ to international ports are not affected by the restrictions. Domestic services are not impacted.
According to Woods, "our number one priority is stopping the virus at the border, so everyone must to go into quarantine or managed isolation. The government is also talking to other airlines about managing flows."
Justin Tighe-Umbers, executive director of the Board of Airline Representatives NZ, said its members want to better understand what capacity the government has for quarantine and isolation, so they can structure their schedules efficiently.
"Airlines are prepared to help the government solve its temporary quarantine/isolation accommodation supply problem and will be limiting inbound passengers as needed," he said.
However, "there is a need for a structured process to manage quarantine, so airlines can set their schedules with confidence."
Military operation
Last month, Woods was given ministerial responsibility for overseeing the managed isolation and quarantine facilities and assistant defence chief Air Commodore Darryn Webb was tasked with running the operation after failures at the border saw two people infected with Covid-19 travel unaccompanied from Auckland to Wellington.
"We currently have nearly 6,000 people in our 28 managed isolation facilities and are scaling up more spaces all the time, but we need to do so safely and new facilities need to be watertight before they are opened," Webb said.
New Zealand detected two new cases of Covid-19 today in managed isolation after one case was reported Monday.
There are now 22 active cases, all in managed isolation. There is no community transmission, according to Health Minister Chris Hipkins.
Webb said the temporary measures will ease the current demand on facilities while additional supply is brought on line.
In the past three weeks, the government has brought on 10 new facilities, expanding capacity for 2,000 more people.
More capacity coming
Hipkins told a press conference that work is underway to increase capacity with another 700 beds expected to come onstream this week.
"We are adding new beds as much as we can," he said in his first Covid-19 press conference as health minister since David Clark resigned the portfolio.
"We do have a responsibility to ensure that New Zealanders returning home, can return home," said Hipkins.
According to Webb, "the pause on new bookings will be short-term, and allows us to increase supply to match forecasted demand over the coming weeks."
Arrivals have continued to increase in recent weeks, with 5,846 people in managed isolation at July 4, according to the government data.
More than 26,639 people have been through managed isolation and quarantine since March 26.
