Police have been made aware of the incident by health authorities.
"While this a health-led matter, police are currently working with Waitematā DHB to ascertain whether any breaches of the Health Order have occurred," a police spokesman said.
An email this morning to Waitemata DHB staff said that a "small number of colleagues have been temporarily stood down from work after coming into contact with a member of the public who has tested positive for Covid-19".
"These North Shore Hospital-based staff will undergo testing and will be away from work until they are cleared to return. This situation has come about after a man acted evasively to breach our strict alert level 4 hospital visitor rules on 16 September.
"He bypassed front-of-house screening processes while staff were assisting another person and hid from security staff before running into a lift.
"This person has acted deceptively to break the rules everyone else has followed and potentially exposed people to the virus in the process," an email to staff said.