Faulkner has been included as Australia seek a replacement for the injured Shane Watson in the two-Test series.
Watson was set to be replaced by 22-year-old Mitchell Marsh, but he is in doubt with a hamstring injury, meaning Faulkner will remain in the Middle East on standby.
Cricket Australia announced Faulkner's inclusion after Friday's second one-day international, which the tourists won by five wickets.
The Tasmanian took 1-27 off seven overs before adding 26 not out in Australia's successful chase, that saw them take an unassailable 2-0 lead in the three-match series.
The addition of Faulkner means Australia have 16 players in their Test squad.
Faulkner has played one Test for Australia, taking six wickets against England at The Oval in August last year.
He was included in Australia's squad for their Test tour of South Africa but a knee injury forced him to withdraw.