He will definitely miss the upcoming limited-overs series against Pakistan, which starts in Auckland on Friday, and is a major doubt for the three one-dayers against Australia.
The first test against the transtasman rivals at Wellington starts in 33 days.
It would be a huge blow to New Zealand's chances if Southee misses the series because, without him to complement Trent Boult as new ball partners, the Black Caps' potency will be threatened.
The pair have been a cornerstone to New Zealand's recent test success, including going undefeated in eight of their last nine series.
In 32 tests together, Southee has 126 wickets at 27.99 and Boult 132 at 26.97. Southee gets a wicket every 58 balls; Boult every 55.
Their left-arm/right-arm partnership makes a case for challenging Richard Hadlee and Richard Collinge as New Zealand's greatest pair with the new ball.
In 13 tests together in the 1970s, Hadlee took 61 wickets at 27.93 and Richard Collinge 52 at 27.82. Southee was the most successful bowler in the test series against Sri Lanka, taking 13 wickets at 16.30, but struggled against Australia with six wickets at 60.50.
If Southee is ruled out, the onus goes on Doug Bracewell, Neil Wagner and Matt Henry to fill the void. Each has shown form in various formats this season.
"It's reassuring to have those options," McMillan said. "One of the great things from this [ODI] series [against Sri Lanka] has been the form of Matt Henry [who picked up 13 wickets at 9.38 and an economy rate of 4.11]. That shows a confidence to come into the set-up and perform straight away."
Southee's absence would offer respite for the Australians, who are contemplating the prospect of the ball hooping about in New Zealand conditions.
"Not too dissimilar to England," opening batsman David Warner predicted. "But I think the wickets are probably going to be a bit greener."
Australia were skittled for 60 at Trent Bridge last year, when pace bowler Stuart Broad took eight for 15.
"We've got to go over there and play with the same intent we do here," Warner said. "The swinging conditions are probably going to favour them."
Warner's team have no warm-up games in New Zealand, with Cricket Australia instead scheduling a Sheffield Shield match between NSW and Western Australia at Lincoln.
Many of Australia's test players are likely to play in the simultaneous three-match ODI series.
Black Caps' schedule
Jan 10: Sri Lanka, Eden Park (2nd T20)
Jan 15: Pakistan, Eden Park (1st T20)
Jan 17: Pakistan, Hamilton (2nd T20)
Jan 22: Pakistan, Wellington (3rd T20)
Jan 25: Pakistan, Wellington (1st ODI)
Jan 28: Pakistan, Napier (2nd ODI)
Jan 31: Pakistan, Eden Park (3rd ODI)
Feb 3: Australia, Eden Park (1st ODI)
Feb 6: Australia, Wellington (2nd ODI)
Feb 8: Australia, Hamilton (3rd ODI)
Feb 12-16: Australia, Wellington (1st test)
Feb 20-24: Australia, Christchurch (2nd test)
- additional reporting AAP