He suffered a hamstring injury in Wednesday's match, comprehensively won by New Zealand by 159 runs, and is to be replaced by Marcus Stoinis.
The left-arm quick, who was also the man of the match when Australia beat New Zealand in the World Cup final last year, was one of the few Australians to distinguish himself when the two sides met in an ODI for the first time since on Wednesday.
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Faulkner took two wickets and contributed the second highest score of 36 with the bat as the world champions folded for 148 in reply to New Zealand's 307-8.
"Unfortunately, with the short turnaround between games we do not believe he will recover in time to take any further part in the series," Australian team doctor Alex Kountouris said.
"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."
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Faulkner's departure adds to a growing list of injured in the Australian squad with Mitchell Starc, Pat Cummins, Nathan Coulter-Nile and Aaron Finch missing from the New Zealand series as well as coach Darren Lehmann.
Stoinis, who will join the Australian squad in time for the second ODI in Wellington on Saturday is an all-rounder who has only played one ODI and one Twenty20 in the past year.
After New Zealand posted a score in excess of 300, with Martin Guptill and Henry Nicholls both scoring half-centuries, Australia were quickly on the ropes at 41-6 before Faulkner and Matthew Wade added 79, an Australian seventh wicket record partnership against New Zealand.
Wade was Australia's top scorer with 37 while for New Zealand Trent Boult took three for 38 and Matt Henry finished with three for 41.
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