De Zorzi replaces seamer Kyle Abbott, who will miss the SA20 due to injury.
The 26-year-old De Zorzi recently scored a maiden ODI hundred against India and made 28 in the first Test in Centurion.
He was expected to open the batting in New Zealand for a Proteas Test team that will be without SA20 players due to a scheduling clash, as well as the experienced Dean Elgar, who will retire from international cricket after the second Test against India at Newlands.
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