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.
With Foster, Plumtree and McLeod all out, Greg Feek and Brad Mooar are set to take charge of the hands on running of the team, with Schmidt brought in to assist.
"Joe will come in for Tuesday and Thursday's training this week, and we're really grateful to have his help," Foster said.
"We've planned for this kind of disruption and we've got back-up plans and people on standby. Joe was one of those people we could call on.
"I've got every confidence in our coaching group and in our senior leaders who are all stepping up in what's a massive test for us."
Foster said he's confident in the team's ability to carry on preparing for the first test, full steam ahead.
"We've had a plan for this happening, and it's a great opportunity for the wider coaching group and the senior players, who will be highly motivated to step up."
"We have learned how to cope with the unexpected, like everyone has over the past couple of years. I will still be working alongside the coaches and team via Zoom and I have huge faith in the coaching group and the players."
"We have structures in place and everyone is working together."
The Crusaders midfielder Braydon Ennor has joined the squad.
It's far from ideal for the All Blacks, who often start slowly in their first test of the year, and are desperate to win this weekend, after being defeated by Ireland in Dublin last November.
The 36-man All Blacks spent last week in camp in Northland before relocating to Auckland ahead of the opening test.