Fleming stood down as the Black Caps one-day captain to concentrate on his Test career following New Zealand's World Cup semi-final loss to Sri Lanka earlier this year and selectors are looking to Vettori to fill the void.
New Zealand coach John Bracewell said including Fleming in the squad travelling to South Africa in September could have proved a distraction.
"This is the first opportunity for Daniel to captain the team abroad and we wanted to ensure that Daniel and the team were not looking to him (Fleming) for leadership," Bracewell said.
Vettori has already expressed his interest in captaining the one-day side in the absence of Fleming and his installation as Twenty20 skipper signals a changing of the guard.
While the spinner has acted as stand-in captain in New Zealand when Fleming has been unavailable, the Twenty20 tournament is the first time he has been handed the skipper's armband overseas.
The New Zealand squad included two new caps in all rounders Nathan McCullum and Bradley Scott.
Wicketkeeper Gareth Hopkins also earned a recall as back-up to Brendon McCullum.
New Zealand's Twenty20 squad: Daniel Vettori (Captain), Shane Bond, Peter Fulton, Mark Gillespie, Gareth Hopkins, Chris Martin, Craig McMillan, Brendon McCullum, Nathan McCullum, Jacob Oram, Jeetan Patel, Bradley Scott, Scott Styris (subject to fitness), Ross Taylor, Lou Vincent.