The 20-year-old, who featured for Wales Under 20 and Sevens sides in 2012/13, replaces the injured Jonathan Davies in the midfield.
Jenkins will face Argentina for the sixth time this weekend and will feature in the front-row alongside Ospreys hooker Richard Hibbard and Rhodri Jones (Scarlets) who replaces the injured Adam Jones.
Bradley Davies (Blues) and Alun Wyn Jones (Ospreys) continue their partnership in the second-row.
In the back-row Ospreys flanker Justin Tipuric comes into the side for the injured Dan Lydiate. Lydiate injured his ankle in the defeat to the Springboks and has been ruled out of the second autumn tie. Tipuric will play at openside flanker with captain Sam Warburton (Blues) switching to blindside.
The duo are joined by Toby Faletau (Dragons), reuniting the back-row which faced England in the final RBS 6 Nations game earlier this year, which saw Wales retain the Championship in dramatic style at the Millennium Stadium.
The back-three is the same that started the game against South Africa last time out with George North (Northampton Saints) and Liam Williams (Scarlets) on the wing and Leigh Halfpenny (Blues), who passed the 300 point-haul for Wales last weekend, at full-back.
Leigh Halfpenny (Blues), George North (Northampton Saints), Cory Allen (Blues), Scott Williams (Scarlets), Liam Williams (Scarlets), Dan Biggar (Ospreys), Mike Phillips (Unattached); Gethin Jenkins (Blues), Richard Hibbard (Ospreys), Rhodri Jones (Scarlets), Bradley Davies (Blues), Alun Wyn Jones (Ospreys), Sam Warburton (Blues - Capt.), Justin Tipuric (Ospreys), Toby Faletau (Dragons).
Replacements: Ken Owens (Scarlets), Paul James (Bath), Samson Lee (Scarlets), Luke Charteris (Perpignan), Ryan Jones (Ospreys), Lloyd Williams (Blues), James Hook (Perpignan), Ashley Beck (Ospreys)