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.
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