Santner, recovering from abdominal surgery, is targeting a return later in the month against England, New Zealand Cricket (NZC) said on Wednesday.
In his absence, Bracewell will lead the side for the three-match series at Bay Oval in Mount Maunganui, starting October 1.
Explosive opener Finn Allen is sidelined with a foot injury, while pace trio Lockie Ferguson (hamstring), Adam Milne (ankle), and Will O'Rourke (back), and all-rounder Glenn Phillips (groin) are also unavailable.
Top batter Kane Williamson is skipping the series, NZC said earlier in the week.
Despite the setbacks, New Zealand's pace stocks have been bolstered by the return of Kyle Jamieson and Ben Sears.
Jamieson missed the Zimbabwe tour for the birth of his first child, while Sears returns from a side injury for the Chappell-Hadlee series.
They join Matt Henry, world number one T20I bowler Jacob Duffy, and Canterbury quick Zak Foulkes in the seam attack.
Bracewell, who has led New Zealand to six wins in 10 T20Is, is aiming to reclaim the Chappell-Hadlee Trophy for New Zealand for the first time since 2016.
"It's a great way to start the summer," Bracewell said in a statement.
"The rivalry is massive, and we're motivated to bring the trophy home."
Young batter Bevon Jacobs retains his spot after an unbeaten 44 on debut in Zimbabwe, while legspinner Ish Sodhi, who recently became the third men's player to reach 150 T20I wickets, will feature as the sole specialist slow bowler.
The series marks 20 years since the first ever men's T20I and will be played entirely at Bay Oval.
