Pocock was substituted in the 36th minute and while it appeared tactical to allow James Slipper to temporarily replace the sin-binned Scott Sio, the number eight did not return when the Wallabies had their full complement back.
Television showed the 28-year-old nursing his hand and appearing to be in pain during the match. Coach Michael Cheika said it had swollen up after the game.
"He wanted to play through, I had to take him off," Cheika said post-match.
The Wallabies confirmed on Sunday that scans had confirmed the break and he would miss the final two games against South Africa in Pretoria on Oct. 1 and then Argentina in London the following week.
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It was likely he would return for the final Bledisloe Cup match against the All Blacks in Auckland on Oct. 22, the team said.
Melbourne Rebels loose forward Sean McMahon could be considered to replace Pocock after impressing from off the bench against the Pumas but his Super Rugby team mate Lopeti Timani, who made his test debut in the reserves, offers a more bulky number eight option.
"Sean McMahon was outstanding with a couple of carries, which got us on the front foot," Cheika said.
(Reporting by Greg Stutchbury in Wellington; Editing by Ian Ransom)
