Elsewhere in the bowling ranks, Ish Sodhi returns to the squad after missing England’s tour, having featured in the 2-0 series loss to Australia at Mount Maunganui to start the summer.
“Kyle’s been back bowling this week and is tracking nicely for this series,” coach Rob Walter said.
“Nathan’s made an impressive start to his international career in the test and ODI formats and we back him to do the job if he gets his T20 chance in this series.
“Ish is our most-capped T20I [T20 International] player and it’s always great to be able to add his skills, energy and experience to the group.
“Matt has played every game for the Black caps since the tour to Zimbabwe in July, so it’s the right moment for him to have a short break and the fact he will also get some time to rehab his calf is another upside.”
However, there is no room in the squad for Blair Tickner, despite his man-of-the-series efforts against England, with his last T20I coming in April 2023.
In the batting group, Kane Williamson was not considered after his retirement earlier on Sunday, while Bevon Jacobs has also been dropped after only featuring once to start the season.
Finn Allen and Glenn Phillips remain unavailable with the respective foot and groin injuries suffered during American Major League Cricket earlier this year.
The five-match series begins in Auckland on Wednesday.
Black Caps squad: Mitchell Santner (c), Michael Bracewell, Mark Chapman, Devon Conway, Jacob Duffy, Zak Foulkes, Kyle Jamieson, Daryl Mitchell, Jimmy Neesham, Rachin Ravindra, Tim Robinson, Tim Seifert (wk), Nathan Smith, Ish Sodhi