The 25-year-old suffered a hamstring complaint during the opening encounter at Eden Park earlier today, which the Aussies lost by 159 runs.
"James reported increased stiffness in his right hamstring during the first innings and found it difficult running during our batting innings," Cricket Australia's doctor Alex Kountouris told reporters.
"Unfortunately, with the short turnaround between games we do not believe he will recover in time to take any further part in the series. As a result, he will return to Melbourne tomorrow to have scans and start rehabilitation."
Right-armer Marcus Stoinis has been drafted in as a replacement.