Fellow backs Damian de Allende, Cheslin Kolbe and Willie le Roux, and forwards Bongi Mbonambi, Frans Malherbe and Pieter-Steph du Toit are also given a break by coach Rassie Erasmus.
They are all set to rejoin the squad when the Boks return home for the final Test in the Rugby Championship against Argentina in Nelspruit on September 28.
Lock forward Eben Etzebeth is included in the squad putting him in line to equal Victor Matfield's record of 127 caps for the Springboks in Santiago del Estero.
Seeking only a second Rugby Championship title in 12 attempts, leaders South Africa will clinch the title if they win at the Estadio Unico.
South Africa beat New Zealand 18-12 last Saturday to reach 18 points from four matches. Argentina, who scored nine tries in a 67-27 thrashing of Australia, have eight.
Defending champions New Zealand (seven points) and Australia (four) cannot overtake the Springboks with two rounds remaining.
Feinberg-Mngomezulu debuted off the bench against Wales in London last June and is the only Springbok to play in all eight Tests this year.
He is the leading scorer for the world champions, kicking 14 conversions and eight penalties for 52 points, 11 more than fellow playmaker Handre Pollard.
Pollard and Manie Libbok, who has featured in only two Tests this season, will be the fly-half options for Erasmus in Argentina.
"The players we decided to rest have really done their bit this season and their bodies deserve a break," said the coach.
"So we thought the best for them would be to enjoy a break and spend time with their families before joining us (for the final round).
"All of the players in the 28-man squad have been in the set-up this year and proved their worth, so we are delighted to give them an opportunity to face Argentina on their home ground.
"We believe playing against Argentina in Santiago, where we are expecting a massive encounter in front of a hostile crowd, will serve as a great test for this group of players."
Squad
Props: Thomas du Toit, Vincent Koch, Ox Nche, Gerhard Steenekamp
Hookers: Johan Grobbelaar, Malcolm Marx
Locks: Eben Etzebeth, Nicolaas Janse van Rensburg, Salmaan Moerat, Ruan Nortje
Loose forwards: Ben-Jason Dixon, Siya Kolisi, Elrigh Louw, Kwagga Smith, Marco van Staden, Jasper Wiese
Utility forward: Jan-Hendrik Wessels
Scrumhalves: Jaden Hendrikse, Cobus Reinach, Grant Williams
Fly-halves: Manie Libbok, Handre Pollard
Centres: Lukhanyo Am, Jesse Kriel
Outside backs: Kurt-Lee Arendse, Aphelele Fassi, Makazole Mapimpi
Utility back: Canan Moodie
