Rob Walter, who replaced Gary Stead as coach last month, named his first Test squad on Tuesday, awarding a call-up to uncapped young fast bowler Matt Fisher and recalling experienced hands Ajaz Patel and Henry Nicholls.
"Kane and Michael were up front with New Zealand Cricket about their availability for this tour during the contracting process," Walter said in a news release.
"While all Test matches are hugely special and important, the fact these Tests aren't part of the World Test Championship did influence the discussions on this occasion.
"We will obviously miss their talent and class, but it allows an opportunity to others and we're lucky to be able to call on the likes of Ajaz and Henry, who are both proven performers at Test level."
Allrounder Bracewell has been allowed to miss the tour to play in The Hundred in England, while paceman Kyle Jamieson has elected to stay in New Zealand for the birth of his first child.
Jamieson's absence offers potential opportunities for Fisher and Jacob Duffy, who has played short-format matches for New Zealand but is yet to win a Test cap, in the two matches in Bulawayo in late July and early August.
NEW ZEALAND TEST SQUAD: Tom Latham (captain), Tom Blundell, Devon Conway, Jacob Duffy, Matt Fisher, Matt Henry, Daryl Mitchell, Henry Nicholls, Will O'Rourke, Ajaz Patel, Glenn Phillips, Rachin Ravindra, Mitch Santner, Nathan Smith, Will Young
