Jones, 31, was forced to fly home from the national squad training camp in Poland last week for scans on his troublesome shoulder.
Having reviewed the results of those scans, the Wales medical team have decided Jones needs a further period of rest and will sit out Saturday's Millennium Stadium engagement with the Pumas, although he is expected to be available for selection when the Six Nations champions take on Samoa on Friday week.
Jones' shoulder problem is the latest injury misfortune for Wales ahead of an autumn campaign that also includes fixtures against world champions New Zealand and Australia.
Newport Gwent Dragons flanker Dan Lydiate is a long-term absentee after breaking and dislocating his ankle on regional duty.
And the key figure of tighthead prop Adam Jones will also sit out the quartet of games due to a knee injury.
With Ryan Jones and Lydiate sidelined, there may be an opportunity for Scarlets flanker Aaron Shingler to stake a claim on the blindside of the scrum, with interim head coach Rob Howley also having a potential option of moving skipper Sam Warburton into the number six role and including Ospreys openside Justin Tipuric at number seven.
Wales will name their team to face Argentina on Tuesday.
Wales assistant coach Robin McBryde said: "We took the decision out in Poland, we were aware Ryan had a niggle with his shoulder coming out to Poland so we thought it would be wise to get in there early and investigate if it was anything serious.
"Happily enough that isn't the case, but it is a case of doing quite a bit of rehab work for the remainder of this week in order for him to be fit for next week's match against Samoa, which is positive news."
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