The series will clash with CSA's domestic Twenty20 competition, which is seen as vital to the future financial health of the organisation.
With the country's leading players told to stay at home uncapped Neil Brand will captain the overlapping tour to New Zealand.
Only two players from the South African XI that defeated top-ranked India by an innings and 32 runs in the first Test of their current series last week, David Bedingham and Keegan Petersen, will tour.
CSA insists this is a one-off scenario with no fixture clashes in future, but the decision has drawn criticism from several quarters, including former Australia captain Steve Waugh.
"CSA has the utmost respect for the Test format as the pinnacle of the game we love," the organisation said in a statement on Tuesday.
"The dates for this tour were set when the Future Tours Programme (FTP) for 2023-2027 was finalised in 2022.
"The window for the SA20 had not been determined at that stage. Once it became apparent that there would be a clash, we made every effort to find another mutually suitable timeslot for this series in consultation with New Zealand Cricket.
"Regrettably the constraints imposed by the global cricket calendar rendered this impossible, as the games must be played before April 2025 as part of the World Test Championship.
"Our schedule for the remainder of the FTP has been managed to ensure that there will not be any further clashes between our bilateral commitments and the SA20."
