Woods, who is the MP for Wigram, will work alongside Air Commodore Digby Webb, who was this week put in charge of the facilities and operation after the border blunder which saw two British women to leave and later test positive for Covid-19.
The Ministry of Business, Innovation and Employment will become the lead agency.
It's understood Woods will continue to oversee operations in the long-term when the military eventually steps back from its current responsibility.
A Government spokesperson says this is a new role, and Woods is not taking the responsibility away from anyone.
It's understood Woods has been given the responsibility because of her work with the housing portfolio and work with MBIE as Research, Science and Innovation Minister.
On Wednesday, Ardern announced the Defence Force - under Webb - would be put in charge of quarantine and isolation facilities.
Webb will undertake an audit of all the existing systems and written protocols to ensure they were being fully implemented.
He will also have access to the country's military logistics, operational expertise and - if needed - have the power to bring in military personnel to assist with running the facilities.
