A calf injury has kept Buttler on the sidelines since July and a recent setback - which saw him miss Lancashire's Vitality Blast quarter-final - has extended his lay-off.
Salt, who deputised for Buttler at Manchester Originals in this season's Hundred tournament, will lead his country for the first time at the Utilita Bowl on Wednesday, before games at Sophia Gardens and his home ground of Emirates Old Trafford.
The five-match ODI series starts on September 19, so Buttler has two weeks to recover.
England have already started blooding a new generation of leaders this summer, with Ben Stokes' torn hamstring allowing Ollie Pope to take charge of the ongoing Test series against Sri Lanka.
Harry Brook has served as Pope's vice-captain and is expected to be named as skipper for the one-day internationals against Australia, should Buttler's absence continue.
England have tweaked their squads to cover for Buttler, adding Surrey allrounder Jamie Overton to the T20 squad and naming Jordan Cox as cover for the 50-over leg.
Marcus Trescothick will serve as interim head coach against Australia, with Test coach Brendon McCullum taking over all formats in the new year.
ENGLAND T20 SQUAD: Phil Salt (captain), Jofra Archer, Jacob Bethell, Brydon Carse, Jordan Cox, Sam Curran, Josh Hull, Will Jacks, Liam Livingstone, Saqib Mahmood, Dan Mousley, Jamie Overton, Adil Rashid, Reece Topley, John Turner
ENGLAND ODI SQUAD: Jos Buttler (captain), Jofra Archer, Gus Atkinson, Jacob Bethell, Harry Brook, Brydon Carse, Jordan Cox, Ben Duckett, Josh Hull, Will Jacks, Matthew Potts, Adil Rashid, Phil Salt, Jamie Smith, Reece Topley, John Turner
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