Jones went off late in the first half and his uncapped Ospreys colleague Lloyd Peers has been called up to train with the Wales squad as temporary cover.
Centre Jamie Roberts, though, could be in the selection mix for next Friday night's Millennium Stadium appointment with Samoa.
Roberts suffered what the Welsh Rugby Union say was "mild concussion" against the Pumas and is currently following the required protocols.
Back-row forward Ryan Jones (shoulder) and centre Ashley Beck (hip) are on course to train fully this week, but Scarlets centre Jonathan Davies is still taking only a limited part in training due to a groin problem.
Prop Adam Jones and flanker Dan Lydiate had already been sidelined from the entire series prior to the Argentina game because of knee and ankle injuries respectively.
The announcement of the team to face Samoa has now been put back 24 hours to Wednesday lunchtime.
The WRU said this would "allow coaches and medical staff further time to assess injuries and player recovery".
Wales' 26-12 loss to Argentina was their heaviest home defeat for three years and worst anywhere for 22 Tests.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
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The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.