Folau fell awkwardly after an aerial contest during the second half of the 38-13 loss at Sydney's Olympic stadium and hobbled off the ground.
The dual international's loss for next Saturday's match is a huge blow for the Wallabies, who have not won at Eden Park in 32 years.
"He just got a small tear in a muscle, right down low. Quite rare, really, but it's actually not a long-term injury at all," Wallabies coach Michael Cheika told reporters at Sydney airport on Sunday ahead of the team's flight to Auckland.
"It's just a lot of swelling. We'll be hopeful he'll be back for the first game in Brisbane."
Australia play the third match of the Rugby Championship against South Africa at Brisbane's Lang Park on Sept. 8.
The Springboks beat Argentina 34-21 in their Rugby Championship opener on Saturday.
After Folau came off, replacement back Jack Maddocks scored the Wallabies' sole try in a lively test debut and Cheika said the Melbourne Rebel could be ready to step up.
“I thought he did OK out there when he went on,” Cheika said.
“I haven’t had a good look at it but he wouldn’t have been on the bench if we didn’t think he was ready to play.
“He got a few touches and got a try as well so, yeah, I would imagine he would be there.
“We’ve also got Tom Banks, who’s an out-and-out fullback so we’ll see where we end up."
Cheika could also opt for inside centre Kurtley Beale to switch to fullback, where he has plenty of experience, and promote Matt Toomua from the reserves to the number 12 jersey.
(Reporting by Ian Ransom in Melbourne; Editing by Peter Rutherford)
