Stoinis, who had sustained a "low-level side strain", would undergo rehabilitation in Perth leading into the team's tour of India later this month.
Nathan Ellis has joined the squad as Australia push for a 3-0 series sweep against their trans-Tasman rivals.
"David Warner has been released from the squad considering a heavy workload over the next 12 months and the series being secured," the team said in a statement.
Australia white-ball captain Aaron Finch will quit the one-day format after Sunday's match in Cairns.