Cricket Australia replaced him with pace bowler Andrew Tye for the series which includes three ODIs and three T20 Internationals.
Cricket Australia on Wednesday said Richardson withdrew from the squad to be with his wife and their newborn son in Adelaide.
Kane Richardson had withdrawn from the upcoming edition of the IPL earlier this week, with Adam Zampa replacing him at RCB.
The reason behind the change is yet to disclosed by the franchise.
The ICC, on Wednesday, said it will wait for another month before taking a call on the T20 World Cup, scheduled to be held in Australia in October-November.
Richardson had an operation on his right shoulder late last month, the same shoulder he dislocated during a match against Pakistan more than a year ago that sidelined him for six months, cricket.com.au reported.
Seventeen Australians hold Indian Premier League contracts, which was scheduled to start on March 29 but has been suspended till April 15.
Kane Richardson had been tested for coronavirus after showing symptoms of the disease.
Australia bowler Kane Richardson has been quarantined after showing symptoms of coronavirus.
Richardson said the Virat Kohli-led Indians were the favourites at home, calling his team the underdogs for the three-match ODI series
Stoinis apologised for his behaviour and said: "I got caught in the moment and took it too far."
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