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The 30-year-old pacer had missed the third ODI due to back and rib niggles but returned to claim two wickets in the 11-run loss in the first T20I in Canberra on Friday.
He had arrived in Sydney on Saturday but soon left the team bubble after learning about a family illness.
“There is nothing in the world more important than family and in this case Mitch is no exception,” said Australia head coach Justin Langer said in a statement.
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The second and third T20Is are scheduled on Sunday and Tuesday.
The opening Day-Night Test starts in Adelaide from December 17 and it is not clear when Starc will be rejoining the team.
Australia is dealing with a spate of injuries with David Warner and Ashton Agar ruled out of the limited-overs series with injuries, while Pat Cummins has been rested for the final ODI and the T20 series as part of his workload management.
All-rounder Marcus Stoinis is still with the squad despite not featuring in any match after suffering a side injury in the first ODI.
Skipper Aaron Finch is also a doubtful starter after he picked up a niggle on his hip during the first T20I.