Sharpe, who is set to retire after the tournament, takes over the responsibility after Will Genia became the latest player struck by the "captain's curse".
Genia is facing six months out, with previous skippers David Pocock and James Horwill having also suffered season-ending injuries.
"To have the privilege of leading Australia in the first ever test to be played on the Gold Coast is an experience I will always treasure," said Sharpe.
"It's important we keep our focus as a team, build on what we achieved last weekend in Perth, and add to that momentum.
"No one else in the squad has played Argentina before but I have and they will be tough, incredibly passionate and uncompromising.
"You only have to look at what they have achieved to date in their tournament matches to see what a threat they will be."
The absence of Genia means Nick Phipps will start at scrum-half as one of a handful of changes.
Pat McCabe returns from injury to start at inside centre, with Berrick Barnes switching to full-back for the benched Kurtley Beale.
Kane Douglas will make his Test debut alongside Sharpe in the second row, with Sitaleki Timani having suffered a hamstring injury in the win over South Africa.
Stephen Moore has been bracketed in on the bench alongside Saia Fainga'a, with the experienced hooker facing a late fitness test on a hamstring injury.
Australia: 15 Berrick Barnes, 14 Dom Shipperley, 13 Adam Ashley-Cooper, 12 Pat McCabe, 11 Digby Ioane, 10 Quade Cooper, 9 Nick Phipps, 8 Radike Samo, 7 Michael Hooper, 6 Dave Dennis, 5 Nathan Sharpe (captain), 4 Kane Douglas, 3 Ben Alexander, 2 Tatafu Polota Nau, 1 Benn Robinson.Replacements: 16 Stephen Moore/Saia Fainga'a, 17 James Slipper, 18 Scott Higginbotham, 19 Liam Gill, 20 Brett Sheehan, 21 Anthony Fainga'a, 22 Kurtley Beale
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