The 23-year-old Schatz had shown "signs of significant swelling" to his right knee, which had initially flared up after Friday's Captain's Run, the team said in a statement early on Saturday.
"Jake has come very close to debuting for Australia on a number of occasions now so on a personal level we are all extremely disappointed to rule him out on matchday," Wallabies coach Ewen McKenzie said.
"Liam has been involved in our opening two Tests so will slot straight back into what we are trying to achieve against the Springboks."
Gill, 21, played off the bench in the Wallabies' two opening losses of the southern hemisphere tournament against New Zealand.
Australia have already lost a number of forwards to injury in the series, including captain James Horwill, who was ruled out this week with a hamstring problem.
Scrum-half Will Genia will lead the Wallabies at Lang Park in the lock's absence.
South Africa head into their match at Lang Park undefeated after two wins against Argentina.
McKenzie also confirmed New South Wales Waratahs lock Sitaleki Timani and backrower Dave Dennis would join the Australia squad in Perth on Sunday ahead of the Wallabies' clash with Argentina next week.