Jones sustained a shoulder injury while Turnbull suffered medial ligament damage to his knee and will be sidelined for at least four weeks.
Wales host Samoa on Friday before taking on world champions New Zealand and Australia.
The WRU said in a statement that Jamie Roberts, who sustained mild concussion against the Pumas, was hopeful of being available for the Samoa game but fellow centre Jonathan Davies, who missed the home loss, was still unable to train fully because of a groin problem.
- Sports & Recreation
- Jamie Roberts