Scarlets flanker Turnbull sustained medial ligament damage to his knee, also during the clash with the Pumas and despite playing on, he is set to be side-lined for a minimum of four weeks, ruling him out of the remaining fixtures at the Millennium Stadium against Samoa, New Zealand and Australia.
Elsewhere, both flanker Ryan Jones and Ospreys' centre Ashley Beck have been fully re-integrated into training today and should be available for selection for Samoa this Friday.
Blues centre Jamie Roberts is continuing with set return to play protocols after suffering mild concussion. He will undertake further individual sessions tomorrow and on Wednesday and is also hopeful of being available for Friday night's clash with the South Sea Islanders.
There has been no change in the situation with Scarlets centre Jonathan Davies who is managing a groin problem and is currently unable to train fully with the squad.
No further call-ups have been made to the Wales squad for the Dove Men Series at this stage.