"Unfortunately, with the short turnaround between games we do not believe he will recover in time to take any further part in the series," said Australia's team doctor Alex Kountouris.
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"As a result, he will return to Melbourne to have scans and start rehabilitation.
"We are hopeful this is only a low grade injury but will know more in the coming days."
Faulkner is among Australia's best lower-order hitters and a clever left arm medium pacer.
It was just the news Australia didn't need after slumping to 41 for six last night, handing New Zealand their biggest ODI win on Eden Park in terms of run margin, and second best against Australia, behind the 1986 match in Adelaide when they rolled the Aussies for 70 and won by 206 runs.
Faulkner took two wickets, one with a sharp return catch to remove Adam Milne, and hit a brisk 36, second top score in Australia's dismal total of 148 in just 24.2 overs last night. The 146 balls Australia's batsmen lasted is the lowest in their ODI history.
Australian captain Steve Smith was bang on after the match when he said his batsmen needed to be more patient as they adjusted to New Zealand conditions.
There was an air of general impatience as they set about chasing down New Zealand's 307 for eight.
Smith himself drove at a wideish ball from Matt Henry and dragged it onto his stumps; Glenn Maxwell, with his team a parlous 40 for four, aimed a lavish drive at Trent Boult second ball and was spectacularly caught at deep extra cover one-handed by Kane Williamson; while George Bailey, dropped by Corey Anderson at short mid wicket, repeated the shot two balls later and Anderson gratefully grabbed his second opportunity having laboured 10 balls over two.
Expect the in-form, but unwanted Usman Khawaja to get his chance at Wellington, most likely at the expense of in-and-out fellow lefthander Shaun Marsh.
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