Head coach Ian Foster, assistants John Plumtree and Scott McLeod and players David Havili and Jack Goodhue are already isolating after testing positive.
Jordan, who was certain to start in Saturday's clash at Auckland's Eden Park, was added to the list of affected players on Tuesday.
The 24-year-old was one of three players remaining in the squad not to have caught COVID. Extra precautions are being taken with the remaining two.
His loss is a major blow to the All Blacks who already face the prospect of a backline reshuffle because of the loss of midfielders Havili and Goodhue. Jordan has scored 17 tries in 13 appearances for New Zealand and scored 10 tries for the Crusaders during their Super Rugby Pacific-winning season.
His place in New Zealand's starting 15 will likely go to teammate Sevu Reece while another Crusader in centre/winger Braydon Ennor has been called into the squad.
Richie Mo'unga also missed training on Tuesday with a stomach bug, but he has not tested positive to COVID and is expected to rejoin the team later this week.
Assistant coaches Greg Feek and Brad Mooar are currently coaching the All Blacks team while Foster, Plumtree and McLeod isolate at home. Former Ireland coach and Kiwi Joe Schmidt, who was due to join the team later this year, has started early to assist the depleted coaching group.
