The teams will contest three 50-over matches at Willowmoore Park in Benoni, followed by a four-day match at JB Marks Oval in Potchefstroom before wrapping up the tour with a second four-day match at Benoni from 14 September.
Marques Ackerman will once again captain the South Africa A team just as he did successfully in West Indies earlier this year.
Rubin Hermann, who recently made his T20I debut in the tri-series in Zimbabwe, has been named in the 50-over squad.
Meanwhile, Proteas-capped batter Zubayr Hamza returns to the SA A setup as part of the four-day squad.
Spinner Tsepo Ndwandwa has earned his maiden South Africa A call-up following impressive performances for the SA Emerging side during their tour to Bangladesh in May.
South Africa A head coach Wadile Gwavu said: "Gerald and Kwena add valuable international experience and skill, and with Bjorn Fortuin unavailable due to a groin injury, Tsepo's selection is well deserved based on his recent performances.
"Playing in our own backyard in familiar conditions is definitely an added advantage, and we're definitely looking forward to competing strongly and building on the momentum we've created."
Gwavu added: "With the team having done well on our recent tour of West Indies, it was important for us to show faith in the majority of that same squad for the upcoming home series against New Zealand.
"I believe that continuity builds trust and confidence among the players, and reinforces the purpose of SA A as a platform for future Proteas.
"I was really impressed with how Marques led the team during the West Indies tour. The entire changeroom wanted to play for him, and that's always a great sign.
"It was an easy and straightforward decision to back him again, and I'm definitely looking forward to working with him on this upcoming tour."
South Africa A 50-over squad: Marques Ackerman (captain), Okuhle Cele, Gerald Coetzee, Jordan Hermann, Rubin Hermann, Tristan Luus, Kwena Maphaka, Rivaldo Moonsamy, Tshepo Moreki, Mihlali Mpongwana, Tsepo Ndwandwa, Nqaba Peter, Sinethemba Qeshile, Andile Simelane, and Jason Smith
South Africa A four-Day squad: Marques Ackerman (captain), Okuhle Cele, Gerald Coetzee, Schalk Engelbrecht, Zubayr Hamza, Jordan Hermann, Tristan Luus, Kwena Maphaka, Rivaldo Moonsamy, Tshepo Moreki, Mihlali Mpongwana, Tsepo Ndwandwa, Sinethemba Qeshile, Lesego Senokwane, Jason Smith, and Codi Yusuf