Tye was part of Australia's squad on their recent limited overs tour of England.
"It was a difficult decision for Kane to make but one which has the complete support of the selectors and the entire playing squad," national selector Trevor Hohns said in a statement.
"Kane wanted to remain in Adelaide with Nyki and their newborn son. We will always support our players and their families; even more so given the challenging environment we are in." The tour by India has been complicated in recent days with a fresh coronavirus outbreak in South Australia, which is to host the first test from Dec. 17.
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The limited overs series, involving three one-day and three Twenty20 matches in Sydney and Canberra, will precede the four tests.
Cricket Australia added that because of the outbreak, D'Arcy Short and Josh Philippe will train with the Australian limited overs squad in Sydney from next week before they join their Big Bash sides.
(Reporting by Greg Stutchbury; Editing by Toby Davis)
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