Hard-hitting batsman McCullum and fast bowler Tim Southee are being rested to recover from a heavy workload since the World Cup.
And with bowler Trent Boult and all-rounder Corey Anderson also unavailable because of injuries, it means there are recalls for Tom Latham, Colin Munro, Jimmy Neesham and Adam Milne.
Neesham and Milne are back having recently recovered from injuries while leg spinner Ish Sodhi has been named for the Zimbabwe leg of the tour just days after being dropped from New Zealand’s list of contracted players.
Fast bowler Doug Bracewell will take Sodhi’s place for the South Africa series.
Coach Mike Hesson said: “We think Ish will be useful on pitches which tend to be slow and take turn, and against a Zimbabwe team stacked with right-handers.
“But we’re unlikely to need a third spinner in South Africa which is why we’ve opted for another seamer in Doug.”
Long term,??McCullum is expected to remain skipper until next year’s World Twenty20 in India when he is likely to retire from international cricket, with 24-year-old Williamson his possible successor.
New Zealand will play three ODIs and a Twenty20 international against Zimbabwe at Harare between August 2 and 9, before moving to South Africa for a brace of T20s and three ODIs August 14 to 26
New Zealand squad: Kane Williamson (c), Doug Bracewell, Grant Elliott, Matt Henry, Martin Guptill, Tom Latham, Mitchell McClenaghan, Nathan McCullum, Adam Milne, Colin Munro, James Neesham, Luke Ronchi, Mitchell Santner, Ish Sodhi, Ross Taylor, Ben Wheeler.