Genia started the match against the Springboks but was forced off the field at halftime because of an injury to his right knee, while Horne aggravated a calf problem during the Wallabies' last-gasp 24-20 win at Lang Park.
Coach Michael Cheika said neither player would travel with the squad to Argentina on Monday but was confident they would be available to face the All Blacks in the first of back-to-back tests against the world champions in Sydney on Aug. 8.
"Will's just got a little bit of bone bruising and a little bit of cartilage on his knee," Cheika told reporters at Brisbane airport on Sunday.
"So he’ll need seven to 10 days off feet and then back into rehab after that. So the Bledisloe series is a realistic mark for him.
"And Rob Horne the same, he's got a small strain in his calf ... he’ll just go rehab and will be back for the Bledisloe as well."
Cheika has summoned winger Nick Cummins and scrumhalf Nic White back from the United States, where they have been promoting Australia's World Cup warm-up match in Chicago, to provide cover.
In other changes to his squad, uncapped winger Taqele Naiyaravoro and lock Rory Arnold will be staying in Australia, while hooker James Hanson and prop Tetera Faulkner, who can cover both sides of the front row, have been brought in.
Australia were second best to South Africa for much of Saturday's match and needed a try after the hooter from Tevita Kuridrani to secure the win.
Cheika said the Wallabies were aware they had to improve ahead of next weekend's game if they were to avoid losing to the Pumas in Mendoza for a second year in a row.
"We're not naive, we know there's a lot of imperfections in our game," Cheika said. "And that's okay, we've just got to keep working and training and preparing as best we can.
"Very pleased with the attitude of the players throughout the game and how they came back from a difficult position.
"Because that's what we're trying to change as well, not just the way we play."
Squad:
Forwards - James Slipper, Scott Sio, Greg Holmes, Sekope Kepu, Stephen Moore, Tatafu Polota-Nau, James Hanson, Rob Simmons, Will Skelton, James Horwill, Dean Mumm, Scott Fardy, Scott Higginbotham, Ben McCalman, Sean McMahon, Michael Hooper, David Pocock.
Backs - Nick Phipps, Nic White, Bernard Foley, Quade Cooper, Matt Toomua, Matt Giteau, Kurtley Beale, Tevita Kuridrani, Adam Ashley-Cooper, Drew Mitchell, Joe Tomane, Nick Cummins, Israel Folau.
(Editing by Peter Rutherford)
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