Kolisi has been battling a hamstring injury and while coach Rassie Erasmus said he was fit to play, the coach has selected the inexperienced Paul de Villiers as blindside flanker ahead of him.
Mercurial Sacha Feinberg-Mngomezulu has been chosen at flyhalf ahead of Manie Libbok, who is on the bench, and the experienced Handre Pollard, linking with scrumhalf Grant Williams.
Inside centre Damian de Allende becomes the 10th Springbok to reach 100 Test caps as he starts alongside Jesse Kriel, while wings Kurt-Lee Arendse and Cheslin Kolbe make up the back three with Damian Willemse.
Malcolm Marx is selected at hooker with Nche and Wilco Louw also in the front row, while Eben Etzebeth and Ruan Nortje are the lock pairing.
De Villiers and Pieter-Steph du Toit, who will captain the side, are at flank and Jasper Wiese at number eight.
"Siya trained well with us this week and, although we could have selected him for this clash, we thought it would be best to select Paul for this weekend's game," Erasmus said.
Saturday's Test is the first of four on successive Saturdays as part of 'Rugby's Greatest Rivalry' series and is followed by clashes in Cape Town, Johannesburg again and then Baltimore in the U.S.
The Springboks have won five of their last six Tests against the All Blacks, including inflicting a record 43-10 defeat on their great rivals last time they met in Wellington.
South Africa: 15-Damian Willemse, 14-Cheslin Kolbe, 13-Jesse Kriel, 12-Damian de Allende, 11-Kurt-Lee Arendse, 10-Sacha Feinberg-Mngomezulu, 9-Grant Williams, 8-Jasper Wiese, 7-Pieter-Steph du Toit (captain), 6-Paul de Villiers, 5-Ruan Nortje, 4-Eben Etzebeth, 3-Wilco Louw, 2-Malcolm Marx, 1-Ox Nche. Replacements: 16-Jan-Hendrik Wessels, 17-Gerhard Steenekamp, 18-Zachary Porthen, 19-Cobus Wiese, 20-Andre Esterhuizen, 21-Marco van Staden, 22-Cobus Reinach, 23-Manie Libbok.