The 24-year-old joins a long casualty list for Australia, who face tough Tests against South Africa in Pretoria on September 29 and Argentina in Rosario a week later to round out the inaugural version of the four nation competition.
Cooper, who has yet to return to top form after his return from surgery on his right knee, had scans in Brisbane on Tuesday which revealed a "small chip of articular cartilage" on the joint.
"While the injury will require an operation to clean up and is to the same knee that was operated on after last year's Rugby World Cup, it is not a long term injury and so may not rule Cooper out of the (November tour)," read a statement.
"A decision on the fly-half's availability for that trip will be made once his rehabilitation is underway."
Berrick Barnes, who played at fullback in last weekend's comeback victory over Argentina on the Gold Coast, is likely to stand-in for Cooper for the next two Tests and the third Bledisloe Cup clash with New Zealand on October 20.