Faulkner, 12th man for the last Test against England and a mooted replacement for injury-troubled bowler Ryan Harris, was hit while batting in the nets.
"James was struck on the right thumb while batting in the nets and was subsequently taken for an X-ray which revealed a fracture of the thumb," said team doctor Peter Brukner said in a statement.
"As a result he will not be available for the third Test. His progress will be monitored for a return to playing duty depending on how quickly the injury heals."
Harris has been hit by a flare-up in a long-standing knee problem on the eve of the third Test in Perth, although captain Michael Clarke said he expects him to play.
Australia are 2-0 up in the five-match series after big wins in Brisbane and Adelaide, and they can regain the Ashes with another victory in Perth.