The in-form Canham pulled up sore following the Wallabies' training session in Perth on Friday and will be replaced by Lukhan Salakaia-Loto in the starting side.
Lachlan Shaw has been added to the bench.
"It is always a big loss when you lose your lineout caller and Canham has been playing some really good footy for us," Wallabies captain Harry Wilson told reporters on Saturday.
Canham's withdrawal is a blow to the Wallabies' bid to continue their unbeaten record under new coach Les Kiss.
While his aerial prowess will be hard to cover, the big-bodied Salakaia-Loto should be equipped to handle the Springboks' renowned physicality.
"Someone like Lukhan coming into the starting team...know how excited he will be and he will be raring to go," Wilson said.
"We know (South Africa) are a team that wants to go through us and they're a big abrasive forward pack.
"To have someone like Lukhan next to you, gives you that bit of confidence and he really relishes those battles."
Australia are hoping to claim their biggest scalp of Kiss' fledgling reign against world number one South Africa, who made 13 changes from their last Test against New Zealand earlier this month.
Since Kiss took over from Joe Schmidt in July, the Wallabies beat Japan in consecutive matches before clinching an away series in Argentina for the first time.
"We know what team they're going to be," Wilson said of South Africa who are coming off a convincing 3-1 series victory over the All Blacks.
"We've watched them very closely play some unbelievable Test footy against the Kiwis.
"There have been a few changes but they've still got 10 World Cup winners, so we're really excited for it."
South Africa have won five of the last six Tests against Australia, including a decisive 30-12 victory at Perth's Optus Stadium in 2024.
Updated Australia squad:
Starters: 15-Tom Wright; 14-Max Jorgensen, 13-Len Ikitau, 12-Hunter Paisami, 11-Joseph-Aukuso Suaalii; 10-Ben Donaldson, 9-Ryan Lonergan; 8-Harry Wilson (capt), 7-Fraser McReight, 6-Rob Valetini; 5-Jeremy Williams, 4-Lukhan Salakaia-Loto; 3-Allan Alaalatoa, 2-Brandon Paenga-Amosa, 1-Angus Bell
Replacements: 16-Billy Pollard, 17-Aidan Ross, 18-Taniela Tupou, 19-Lachlan Shaw, 20-Tom Hooper, 21-Carlo Tizzano, 22-Tate McDermott, 23-Harry Potter
South Africa squad:
Starters: 15-Aphelele Fassi, 14-Edwill van der Merwe, 13-Canan Moodie, 12-Andre Esterhuizen (c), 11-Ethan Hooker, 10-Handre Pollard, 9-Herschel Jantjies, 8-Marco van Staden, 7-Elrigh Louw, 6-Paul de Villiers, 5-Franco Mostert, 4-Eben Etzebeth, 3-Zachary Porthen, 2-Johan Grobbelaar, 1-Jan-Hendrik Wessels
Replacements: 16-Malcolm Marx, 17-Ox Nche, 18-Wilco Louw, 19-Lood de Jager, 20-Jasper Wiese, 21-Morne van den Berg, 22-Sacha Feinberg-Mngomezulu, 23-Quan Horn