The Ospreys back-row is returning home from Wales' training camp in Poland to have scans on what the Welsh Rugby Union said was "an irritable shoulder".
The 31-year-old has been managing the shoulder problem since departing for Spala in Poland with the rest of the Wales squad three days ago.
Wales interim head coach Rob Howley is due to announce his team for the Pumas clash a week on Thursday and Jones appears to be a doubt for the match.
A WRU statement read: "The decision to send Jones home at this time is based on a preference for the facilities available in Wales to accommodate the necessary investigations and give the player the most optimal management plan for his injury.
"Jones remains a full member of the squad and further details of his problem and any repercussions for selection, if at all, will become apparent once the proper investigations have been undertaken."
Wales are already without prop Adam Jones and flanker Dan Lydiate for the entire series, which includes matches against Argentina, Samoa, New Zealand and Australia.
Jones was a strong candidate to replace Lydiate after an impressive start to the season with the Ospreys.
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