With the country amid a COVID-19 lockdown and Australia having restrictions around New Zealanders travelling there, the NZR has decided not to send the team which was due to leave for Perth on Sunday and play the Wallabies there on Saturday week.
NZR has also announced the All Blacks' two home rugby championship against South Africa and the Black Ferns two O'Reilly Cup Tests against the Wallaroos will not be played in New Zealand.
The match in Dunedin would have been the 100th test between the All Blacks and the Springboks.
"Without complete certainty on the team's next movements around The Rugby Championship we felt it was prudent for the team to stay put in New Zealand until SANZAAR have announced the full tournament schedule," NZR chief executive Mark Robinson said in a statement.
"Once the team leaves our shores, they currently can't return until November 23 post their Northern Tour, so given the uncertainty, it makes sense to pause and get more clarity on these fixtures.
"We remain 100 percent committed to playing in the entire Rugby Championship in 2021 and are working closely with SANZAAR to look at a range of options to reschedule these important matches."
Robinson said every effort had been made to keep the scheduled tests against the Springboks and Wallaroos in New Zealand.
"However, after discussions with Government, it is clear that the COVID-19 travel restrictions meant there was no way of bringing the South African and Wallaroos squads into New Zealand and we understand the importance of putting the health and safety of New Zealanders first."
He said SANZAAR would make further announcements around the Rugby Championship schedule in due course.