No8 Jasper Wiese is also missing while he serves a four-week suspension.
South Africa's Championship campaign opens with Tests against Australia in Johannesburg on August 16 and Cape Town on August 23.
Coach Rassie Erasmus said when announcing his squad, "It's always challenging to reduce the squad, especially given how the expanded group of players put up their hands [in July internationals against Italy and Georgia], but we always said we would select a smaller, more manageable squad during the Championship.
"We have also communicated with the standby players [who include Am, de Klerk and Mapimpi], so they know exactly where they stand.
"We probably have three players who can cover each position, which is crucial in a tournament like this. One of our key pillars as a team is to build squad depth, and there is no better way to see what some of the younger players are capable of than to expose them to some of the top teams in the world."
Forwards: Lood de Jager, Pieter-Steph du Toit, Jean-Luc du Preez, Eben Etzebeth, Vincent Koch, Siya Kolisi, Wilco Louw, Malcolm Marx, Bongi Mbonambi, Franco Mostert, Ox Nche, Ruan Nortje, Asenathi Ntlabakanye, Kwagga Smith, RG Snyman, Marnus van der Merwe, Marco van Staden, Boan Venter, Jan-Hendrik Wessels, Cobus Wiese.
Backs: Kurt-Lee Arendse, Damian de Allende, Andre Esterhuizen, Aphelele Fassi, Sacha Feinberg-Mngomezulu, Ethan Hooker, Jesse Kriel, Cheslin Kolbe, Willie le Roux, Manie Libbok, Canan Moodie, Handre Pollard, Cobus Reinach, Edwill van der Merwe, Morne van den Berg, Grant Williams, Damian Willemse.