Scans, taken on Saturday, showed that Carter had suffered a torn medial ligament, an injury that takes 12 weeks to clear.
The second row will miss the rest of the Super rugby season as well as Australia's pre-World Cup matches.
Carter, who started 11 tests for Australia last year, required lengthy treatment on the pitch at Canberra Stadium on Friday night after twisting the joint in the 22-16 victory over the Bulls, which kept the Brumbies in the playoff hunt.
Carter tried to run off the injury but was unable to move freely because of the strain, and was ordered to undergo tests on Saturday.
"Like any test player, international player, it's going to be a loss to your team," Brumbies coach Stephen Larkham told reporters after the match.
"He had a bit of a spell out of the game but I thought the last couple of weeks he's really played exceptionally well.
"But I think we're lucky we've got good experience in the second row with Blake Enever and Rory Arnold.
"I think those guys have gained enough experience throughout the year to be able to fill the shoes that Carts leaves."
The emergence of towering lock Arnold has been a major boost to the Brumbies this year and a Wallabies call-up for the Rugby Championship would not be out of the question.
Lock forward is a department where Australia coach Michael Cheika does not have the resources he has in other areas of his squad.
The Brumbies head to Perth to play Western Force in their penultimate match next weekend before rounding out the regular season at home to the Canterbury Crusaders.
(Reporting by Nick Mulvenney; Editing by John O'Brien)
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