He is due to appear in the Auckland District Court tomorrow.
As the matter was before the courts, police they could not comment further.
The man came from Australia on September 16, and tested negative on day three and day 12 of his stay.
The bedsheet ladder was discovered at 8.20am on Monday by on-site security, said Air Commodore Darryn Webb, head of managed isolation and quarantine.
"At approximately 8.24am as the matter was being investigated, the occupant of the room presented himself at the front gate," Webb said on Monday.
The man was swiftly taken into custody by police.
The man allegedly spent eight hours on the loose visiting different parts of the city.
He was captured on CCTV in Aotea Square at 1am Monday, Webb said yesterday.
"The man has been viewed on CCTV walking in parts of Auckland, from the central city to Newmarket, Epsom, Onehunga and Mt Albert before returning to the facility on Federal St."
Early indications suggested the man broke the security latch on the window to force his way out.
"Security improvements at the facility will be made and include the installation of additional CCTV cameras as well as extra lighting at the likely point of the man's alleged exit," Webb said.
Police had reviewed a range of CCTV, interviewed the man, conducted a scene examination and spoken to staff.
Public Health deemed the Covid-19 risk to the public to be low.
