The Scarlets fly-half, who has won 100 caps, suffered a calf muscle problem during the warm-up before Wales' Twickenham clash against England two weeks ago.
He was not involved in last Saturday's return England fixture, but was then named among the substitutes for Argentina's Millennium Stadium visit.
The Welsh Rugby Union say Jones' absence is a precautionary measure.
"He was considered ready to make a return to action, but after experiencing some further problems at the captain's run at the Millennium Stadium, the decision was taken this morning to air on the side of caution and not risk the player against the Pumas," said the WRU, in a statement.
Scott Williams will take Jones' place on the bench.
Wales coach Warren Gatland has already lost Gavin Henson (wrist), Matthew Rees (neck) and Morgan Stoddart (broken leg) from his World Cup plans.
Prop Gethin Jenkins, meanwhile, is unlikely to recover from a calf injury in time for Wales' World Cup opener against South Africa in Wellington on September 11.
And number eight Ryan Jones, who had been due to captain Wales for a record-equalling 28th time today, is resting a calf problem.
Gatland will name his 30-man World Cup squad at midday on Monday.
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