Non-quarantine travel, which was set to be opened for New Zealanders in Australia on 17 January, would be pushed back until the end of February, Covid-19 Response Minister Chris Hipkins said at a media conference on Tuesday.
The length of stay in MIQ facilities would be temporarily increased from a week to 10 days.
The new Super Rugby Pacific competition will feature five teams each from New Zealand and Australia and two sides representing the Pacific Islands -- Moana Pasifika and Fijian Drua.
New Zealand Rugby (NZR) did not immediately respond to an emailed request for comment.
NZR have said the competition, due to begin on February 18, will proceed even in the event of Covid-19 complications and suggested the schedule could be reworked to play "local" games first and fulfil the cross-border fixtures when borders reopen.
Should border re-opening be delayed further, however, it is unclear what impact that would have on the cross-border games.
The new competition builds on 'Super Rugby Trans-Tasman', which was played between Australia and New Zealand's sides this year.
The earlier version of the Super Rugby competition featuring South African teams and Argentina's Jaguares appears unlikely to be revived following its suspension last year due to the Covid-19 pandemic.
The delayed reopening is also likely to affect A-League football team the Wellington Phoenix, whose men's side had planned on staging nine games in New Zealand from January 29 after playing all fixtures so far in Australia.
Hours before the government's announcement Phoenix coach Ufuk Talay said that the club were not expecting to return home as scheduled.
"Every game is an away game," Talay said. "The whole season will be an away game for us and I think the boys understand that."