He was injured during Australia's 159-run loss to New Zealand at Eden Park in the first One-Day here on Wednesday. Australia will play three One-Days and two Tests in New Zealand. The second match is in Wellington on February 6.
Faulkner was replaced in the squad by young all-rounder Marcus Stoinis.
Cricket Australia's Sports Science and Sport Medicine manager Alex Kountouris said in a release: "James reported increased stiffness in his right hamstring during the first innings tonight and found it difficult running during our batting innings."
"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."
"We are hopeful this is only a low grade injury but will know more in the coming days."
Commenting on the decision to call-up Stoinis, national selector Rod Marsh said: "It's unfortunate that James has suffered this injury but the situation presents another good opportunity for Marcus Stoinis."
"He is a promising young all-rounder who had a taste of international cricket last winter in England, and hopefully this call-up will continue with his development."
Stoinis has played jut a single One-Day so far.