Sharpe had planned to retire after the Super Rugby season but was persuaded by Wallabies coach Robbie Deans to play on in the southern hemisphere tournament.
He now founds himself captaining Australia for a third time in his 109th Test after previously leading the side against New Zealand in 2004 and Samoa the following year.
Sharpe takes the reins from scrumhalf Genia who ruptured a knee ligament in the Wallabies' 26-19 win over South Africa in Perth on Saturday and has been ruled out for the season.
Genia had taken the captaincy from flanker David Pocock, who also suffered a season-ending knee injury against New Zealand in their first match of the championship.
Pocock had in turn taken it from regular captain James Horwill, who was ruled out of the Test season when he sustained a serious hamstring injury during the Super Rugby competition.
"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," Sharpe said.
"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."
After being belted by South Africa 27-6 in their tournament debut in Cape Town, Argentina held the Springboks to a 16-16 draw at home and impressed the All Blacks with their resolve in a fighting 21-5 loss in Wellington.
Deans has had to reshuffle his team constantly this season due to injuries and he sprung a surprise by shifting inside back Berrick Barnes to full-back in place of Kurtley Beale, who was dropped to the bench.
Barnes started the Test season against Scotland at fly-half and has played inside centre against the All Blacks and Springboks, but has never played full-back at international level.
New Zealander Deans said Barnes's goalkicking this season had earned him the start.
"Berrick has good grounding at the back while his ability to take just about every point-scoring opportunity on offer was highlighted once again last weekend," Deans added.
"His presence provides good balance to the backline, while giving us the opportunity to throw Kurtley in where he will be at his most dangerous, against a tiring defensive line as the game opens up and he can get out there with a license to play."
Beale, widely considered one of the best attacking players in world rugby, has suffered a crisis of confidence during the Rugby Championship, with Deans now dropping him twice from the starting side.
The return from injury of inside centre Pat McCabe, whose hard-running style is preferred in the position by Deans, may have also played a part in the backline reshuffle.
Nick Phipps takes over from Genia at scrum-half, while lock Kane Douglas makes his Test debut in place of Sitaleki Timani, who suffered a hamstring injury against the Springboks.
Stephen Moore, a late withdrawal from the starting side against the Springboks, has been bracketed with Saia Fainga'a on the replacements' bench and could earn his Australian record 73rd cap for a hooker if he is passed fit from his hamstring injury.
Australia team: 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