Fast bowling all-rounder Marsh has been ruled out of the remainder of the five-match series with a shoulder injury, which he sustained in Australia's six-wicket loss against Pakistan in the second one-dayer at the Melbourne Cricket Ground on Sunday.
Australia have already added batsman Peter Handscomb to their squad with Chris Lynn ruled out of Thursday's third ODI in Perth due to an ongoing neck injury.
Stoinis has a single one-day international for Australia to his name, against England in 2015.
The 27-year-old will play Melbourne Stars' Big Bash Twenty20 match against Brisbane Heat on Tuesday before he and leg-spinner Adam Zampa, who has been released from the squad to play in the same match, join the one-day team in Perth on Wednesday.
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The series is tied at 1-1 after Australia won the opener in Brisbane by 92 runs before Pakistan bounced back in Melbourne.
(Reporting by Amlan Chakraborty in New Delhi; Editing by John O'Brien)
