British & Irish Lions Stephen Jones, Michael Owen and Martyn Williams, plus Robert Sidoli have all been rested.
Fellow Lions Gareth Thomas, Dwayne Peel, Brent Cockbain and Ryan Jones were all overlooked due to injury.
Wales play Argentina in Puerto Madryn on Sunday, June 11 and Buenos Aires the following Saturday.
Jenkins said: "I have looked at the period leading up to the 2007 World Cup, which includes 16 international matches and I have sought expert opinions and advice from medical staff and conditioning coaches.
"There is no doubt that this summer tour is key to our World Cup aspirations.
"Certain players have not been considered because they are undergoing a period of rehabilitation following injury or operations, others have injuries that need further investigation and possible surgery over the summer.
"There is also a group who are simply in need of rest and a structured conditioning programme leading into a prolonged pre-season programme.
"That process is key if we are to get to September and October with a healthy squad of players who are repaired, re-energised, conditioned and producing performances that they weren't able to last season.
"This is a tremendous opportunity for Duncan and the appointment will give me the chance to see how he handles the responsibility as a potential captain of the future."
The average age of the squad is just 24 years and five months, with no player over the age of 29.
Alun Wyn Jones, at 20 years and eight months, is the youngest player in the squad.
"I am positive about this tour selection. It is a great opportunity to look at some of our top young players and expose them to the challenging environment of an international tour," said Jenkins.
"If you include Chris Czekaj, we will have three current under-21 internationals on tour with us, along with Ian Evans who played a major role in last season's under-21 Grand Slam-winning team which is hugely exciting.
"Rhys Thomas and Richard Hibbard have impressed me recently and I am looking forward to seeing how they perform under the pressure of an international environment.
"All of the selected players have put in impressive performances of late and, while they may not all gain Test experience on this tour, they will all gain a vital taste of what it takes to gain that honour and will add to our options and competitiveness.
"I am confident this group of players can be competitive in Argentina and has the chance of being successful. This is an exciting, young squad and I am hugely looking forward to see how they react."
Wales' 28-man squad for June's two-Test tour of Argentina:
Forwards: Duncan Jones (Ospreys, captain), Gethin Jenkins (Cardiff Blues), Adam Rhys Jones (Ospreys), Rhys Thomas (Newport Gwent Dragons), Huw Bennett (Ospreys), Richard Hibbard (Ospreys), Matthew Rees (Llanelli Scarlets), Luke Charteris (Newport Gwent Dragons), Ian Evans (Ospreys), Ian Gough (Newport Gwent Dragons), Alun Wyn Jones (Ospreys), Gareth Delve (Bath), Dafydd Jones (Llanelli Scarlets), Alix Popham (Llanelli Scarlets), Robin Sowden-Taylor (Cardiff Blues), Gavin Thomas (Llanelli Scarlets).
Backs: Michael Phillips (Cardiff Blues), Andy Williams (Bath), Nicky Robinson (Cardiff Blues), James Hook (Ospreys), Jamie Robinson (Cardiff Blues), Hal Luscombe (Newport Gwent Dragons), Matthew Watkins (Llanelli Scarlets), Gavin Henson (Ospreys), Chris Czekaj (Cardiff Blues), Shane Williams (Ospreys), Mark Jones (Llanelli Scarlets), Lee Byrne (Llanelli Scarlets).