The two batsmen have been given an opportunity to impress following injuries to Ross Taylor and Kane Williamson.
Taylor will miss the entire series against South Africa due to a calf problem, while Williamson (wrist) has been ruled out of Tuesday's opening match at Tauranga's Bay Oval.
Latham, 22 last represented New Zealand's ODI team in November 2013 against Sri Lanka, while the 30-year-old Brownlie will be hoping to make his first international 50-over outing since July 2012.
Black Caps head coach Mike Hesson said: "Tom had a very good tour to the West Indies with the Test team and also impressed in the warm-up match [against Ireland] in Lincoln, while Dean was in strong form on the recent tour to the UK."
Paceman Tim Southee has been passed fit following a shoulder injury, while veteran all-rounder Daniel Vettori could play an ODI for the first time since last June.
After Tuesday's series-opener, New Zealand and South Africa will play a second match in Tauranga on Friday before heading to Hamilton for a third and final contest on October 27.
New Zealand ODI squad to face South Africa: Brendon McCullum (captain), Corey Anderson, Trent Boult, Dean Brownlie, Martin Guptill, Matt Henry, Tom Latham, Mitchell McClenaghan, Nathan McCullum, Kyle Mills, James Neesham, Luke Ronchi, Tim Southee, Daniel Vettori.