Du Plessis injured his right knee early in the Springboks' 27-6 win over the Pumas in Cape Town on August 18.
He was taken for scans during the game, which confirmed the diagnosis of an injury to his medial and anterior cruciate ligaments.
Du Plessis requires surgery and he will be out for the remainder of the season.
Apart from Du Plessis, the match day 22 have been retained and five players added to provide depth - Tiaan Liebenberg and Burden (hookers), Dean Greyling (prop), Juandré Kruger (lock) and Jano Vermaak (scrum-half).
Following the Springboks' return from Argentina, the national selectors will meet to select a touring squad of 28 that will travel to Australia and New Zealand for the third and fourth rounds of the Rugby Championship.
"We only finalised the touring squad after the Test against Argentina at Newlands on Saturday afternoon as we wanted to first assess the injury situation," said Springboks coach Heyneke Meyer. "It's never nice to leave behind players, but we're only permitted to travel with 26 players.
"The players that stay behind will benefit from game time in the Absa Currie Cup and will certainly be in the selection frame when we select the squad for the next leg of the Rugby Championship."
South Africa squad:Forwards: Willem Alberts, Andries Bekker, Craig Burden, Pat Cilliers, Marcell Coetzee, Keegan Daniel, Jannie du Plessis, Eben Etzebeth, Dean Greyling, Juandré Kruger, Tiaan Liebenberg, Tendai Mtawarira, Jacques Potgieter, Adriaan Strauss, Flip van der Merwe.
Backs: Jean de Villiers (captain), JJ Engelbrecht, Bryan Habana, Francois Hougaard, Zane Kirchner, Patrick Lambie, Lwazi Mvovo, Ruan Pienaar, Frans Steyn, Morné Steyn, Jano Vermaak