The all-rounder suffered a hand injury while batting in the WACA ground's nets and was sent for scans on Thursday.
It has now been revealed that the 23-year-old will miss the third match of the series that starts on Thursday after scans showed that he has broken his right thumb.
"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 his thumb," Australia's team doctor Peter Brukner said in a statement.
"As a result he will not be available for the third Test."
Faulkner was 12th man for the first two Tests, which were won by Australia.