Head coach Ian Foster, assistant coaches John Plumtree and midfielders David Havili and Jack Goodhue are already isolating after contracting the virus.
First-five Richie Mo'unga missed Tuesday's training with a stomach bug, but has tested negative for Covid.
Former Ireland coach Joe Schmidt has been called in to help the All Blacks prepare for Saturday's test at a sold out Eden Park.
The quartet are isolating and it's understood they won't re-join the team before Saturday's test at a sold out Eden Park.