Cummins, man of the match on debut against South Africa in Johannesburg a fortnight ago, remains sidelined along with four other Test players who missed the nine-wicket first Test win over the Black Caps at the Gabba.
The only change to the first Test squad is the inclusion of South Australian all-rounder Dan Christian in place of injured Queensland quick Ben Cutting who was 12th man.
Cutting suffered a side strain while bowling in the Sheffield Shield match against Victoria and now joins fellow pacemen Cummins (heel), Ryan Harris (hip), Mitchell Johnson (toe surgery) and all-rounder Shane Watson (hamstring) on the sidelines.
Batsman Shaun Marsh has also been given extra time to overcome a lower back injury, alleviating some pressure on besieged opener Phil Hughes who failed with scores of 10 and seven at the Gabba.
Australia team physiotherapist Alex Kountouris said Cummins, Watson and Marsh were all on track to return in time for the four-Test series against India, starting on Boxing Day at the MCG.
"Pat Cummins is still recovering from the left heel injury sustained during the South Africa Test series," Kountouris said.
"Whilst he is improving, he is still not bowling and is unavailable for the second Test against New Zealand.
"He will continue his rehabilitation in an attempt to be fit for the first Test against India."
In Cummins' absence, Victorian debutant James Pattinson stood up with a man-of-the-match performance in Brisbane, taking 5-27 to rout the Black Caps for 150 in their second innings.
Chief selector John Inverarity said Cutting's injury opened the door for the in-form Christian to provide better balance to the team after captain Michael Clarke was forced to use the part-time medium-pace of Mike Hussey to support his young pace attack in the absence of all-rounder Watson.
"The balance of a team is always enhanced by the presence of an energetic all-rounder who is in good form," Inverarity said.
"James Pattinson's performance on debut will provide a great boost not only the team as a whole but to those who are new to the team in particular."
Australian squad: Michael Clarke (capt), David Warner, Phil Hughes, Usman Khawaja, Ricky Ponting, Mike Hussey, Brad Haddin, Peter Siddle, James Pattinson, Mitchell Starc, Nathan Lyon, Dan Christian.
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