The 23-year-old Tasmanian played in all five one-day internationals throughout January and performed a starring role in the victory at Brisbane, which helped the hosts claim a 4-1 series win.
However, scans taken on Monday have indicated that he will need an operation that will prevent him from featuring in the shorter format, and from travelling for next month's Tests against South Africa.
"James injured his knee during the Australia Day one-day international in Adelaide," Australia physiotherapist Alex Kountouris told reporters.
"He has had subsequent scans and was reviewed by Cricket Australia's medical team and a knee specialist, and will require arthroscopic surgery on Tuesday.
"He will not be available for the upcoming Test tour of South Africa. We are hopeful that he will recover in time to play the Twenty 20 games on that tour and take part in the ICC World Twenty20."
Faulkner has been replaced in the Australia squad by uncapped Hobart native Kane Richardson for the three-match series, which begins at his home ground on Wednesday.