Santner, who led the Kiwis to the T20 World Cup final which they lost to co-hosts India, will only play the first three games of the series at home that starts in Mount Maunganui on Sunday.
Latham will then take over leadership duties for the last two matches in what will be the batters first T20Is in almost three years.
The left-handed Latham, a regular in the other two formats, impressed with the bat for Canterbury in the domestic Super Smash tournament.
Several other players will shift in and out of the squad as the selectors manage the workload ans recovery of some niggles.
Devon Conway is likely to keep wicket for the first three games before Dane Cleaver takes over wicketkeeper duties for the remainder of the series.
New Zealand selector Gavin Larsen said: "We've certainly had to be pragmatic in selecting this squad.
"We're lucky to have strong depth across the different skill-sets which has afforded us the opportunity to rest a few players and introduce some others.
"That provides an excellent opportunity for many to stake their claim for regular inclusion in the T20 team moving forward as we begin a new World Cup cycle."
New Zealand T20I squad: Mitchell Santner (capt) (1-3), Katene Clarke (4-5), Josh Clarkson, Dane Cleaver (wk) (4-5), Devon Conway (wk) (1-3), Lockie Ferguson (2-3), Zak Foulkes, Bevon Jacobs, Kyle Jamieson, Nick Kelly, Tom Latham (capt) (4-5), Jayden Lennox (4-5), Cole McConchie, Jimmy Neesham, Tim Robinson, Ben Sears, Nathan Smith, Ish Sodhi