The 24-year-old Anderson suffered the injury on New Zealand's tour of England and had not recovered sufficiently to shoulder a bowling workload, selector Gavin Larsen said in a statement.
"Corey hasn't been able to recover as quickly as we hoped and we've chosen not to try to rush him back," said Larsen.
"We've always said there were a number of checkpoints for him to meet before our departure date, and we're now in a position to confirm he's not ready.
"With that in mind, it's better for him to continue his rehabilitation."
The 23-year-old Santner, who bowls left-arm spin as opposed to the brisk medium pace of the burly Anderson, impressed in the limited overs portion of New Zealand's tour of England and was included for their series against Zimbabwe and South Africa but had to withdraw with a broken thumb.
"Mitch (is) an all-rounder who can bat at number six or seven and he's also a front-line bowler," Larsen added.
"It's a good opportunity for him. We believe his left-arm spin will add some variety to our options and his batting is well-suited to the conditions expected across the Tasman."
New Zealand will play three tests in Australia, including the first twilight match in Adelaide, where a pink ball will be used. The first test in Brisbane begins on Nov. 5.
The side had an intra-squad trial match in Hamilton last week under lights with a pink ball.
Off-spinner Mark Craig said there was little difference between the pink ball and the white ball used for limited overs matches, but the trial had been good to become accustomed to what to expect under differing conditions.
"It's just a matter of getting used to it, there's no complaints from us," Craig told reporters.
"I find it really similar to the white ball. When it's nice and new it's quite easy to grip and just like any other ball when it gets a bit older."
(Reporting by Greg Stutchbury; Editing by Andrew Both)
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