The squad includes Graeme Smith, who will return as captain provided he is passed fit after missing the third and final Test against Australia because of an injured left ring finger.
He will see a specialist in Johannesburg Tuesday. Selection convenor Haroon Lorgat said his chances of playing were "50-50".
Jacques Kallis will captain the team again if Smith is unfit.
Lorgat said a large squad had been picked because there will be no further domestic cricket in South Africa, so potential back-up players will train with the Test team and be ready to step in if needed.
The same squad was picked for the final Test against Australia.
Lorgat said it was unlikely major changes would be made despite South Africa losing all three home Tests against Australia.
"We have retained the same squad of players after the tough series against Australia, the world's number one team," said Lorgat.
"We believe that the experience will stand them in good stead and they deserve another opportunity against New Zealand. We will, however, monitor performances carefully as we seek to build a successful Test team."
The squad: Graeme Smith (captain), Jacques Kallis (vice-captain), AB de Villiers, Herschelle Gibbs, Ashwell Prince, Jacques Rudolph, Mark Boucher, Shaun Pollock, Nicky Boje, Andre Nel, Makhaya Ntini, Boeta Dippenaar, Andrew Hall, Garnett Kruger, Hashim Amla and Dale Steyn.