The 29-year-old all-rounder had only recently recovered from the injury.
Perry, 29, had torn her hamstring during the Women's Twenty20 World Cup earlier this year and after going through surgery and rehabilitation, had been picked for the limited-overs fixtures versus the White Ferns.
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However, she aggravated the injury while training and didn't take part in the first two T20Is, which Australia won.
It is learnt now that the all-rounder won't feature in the ODI leg of the Kiwis' tour either.
“Unfortunately she had some hamstring awareness and has got a low grade strain, so she won't be available for the rest of this series,” Lanning told reporters, as quoted by Reuters.
“It's a very complex injury, and hard to get the timing on when certain things will happen."
"It's really important to get it right and take the time before we do put her out on the field. Hopefully, it's sooner rather than later, but we'll just have to see how it pans out," she added.