The Leinster player, who has won four caps for the Pumas, was ruled out of the match to celebrate Nelson Mandela's 90th birthday on Saturday after a scan revealed he had torn the meniscus in his left knee.
The medical report from Argentina doctor Guillermo Botto read: "Juan Gomez underwent an MRI scan in the afternoon (Monday) and the result shows the tear of the external meniscus of his left knee.
"His participation in the Test against South Africa is ruled out."
Gomez won three of his four caps this year, as he was part of two Tests against Scotland and another with Italy in June.
Argentina head coach Santiago Phelan has called up Jockey Club Salta prop Juan Figallo as his replacement.
Gomez's withdrawal is the second of the tour after Brive player Pablo Henn was ruled out with a muscle injury. Leicester Tigers prop Marcos Ayerza will replace him.
Argentina squad: M Ledesma (ASM Clermont Auvergne), A Galindo (Beziers), M Carizza (Biarritz), H Agulla (Brive), R Carballo (Castres), M Durand (Champagnat), B Urdapilleta (CUBA), L Borges, F Martin Aramburu, N Vergallo (all Dax), B Stortoni (Glasgow Warriors), H Senillosa (Hindu), JM Nunez Piossek (Huirapuca), J Figallo (Jockey Club Salta), M Ayerza (Leicester Tigers), F Contepomi (Leinster), M Avramovic (Montauban), R Alvarez (Perpignan), JM Fernandez Lobbe (Sale Sharks), A Lalanne (SIC), P Ledesma, JM Leguizamon, R Roncero (all Stade Francais), P Albacete, A Vernet Basualdo (both Stade Toulouse), E Lozada (Toulon).