The prop, seen as one of the few ball-carrying options available to boost the flagging Wales pack, sustained the damage playing for his club against Cardiff on 4 February.
The news means that Ben Evans, vilified for his performance in Wales' defeat in Rome, is almost certain to retain his place as the only fit tighthead in the squad.
Winger Mark Jones is also out with the whiplash injuries he received in the Italian defeat.
Rhys Williams is expected to move up from full-back to replace him, with Swansea's Kevin Morgan taking the 15 shirt.
Neath's Duncan Jones, who is not in Wales coach Steve Hansen's 32-man squad but who has been touted as an option at loosehead prop or hooker, is likely to be out of action for at least six weeks.
He was injured in his club's Welsh Premiership win over Llanelli on Saturday night and is awaiting a scan on suspected damaged knee ligaments.
Wales squad:
Backs: K Morgan (Swansea), R Williams (Cardiff), G Thomas (Bridgend), M Jones (Llanelli), C Morgan (Cardiff), M Watkins (Llanelli), J Robinson (Cardiff), L Davies (Llanelli), T Shanklin (Saracens), M Taylor (Swansea), I Harris (Cardiff), C Sweeney (Pontypridd), G Cooper (Bath), R Powell (Cardiff), D Peel (Llanelli)
Forwards: I Thomas (Llanelli), G Jenkins (Pontypridd), B Evans (Swansea), M Madden (Llanelli), M Davies (Pontypridd), G Williams (Bridgend), R Sidoli (Pontypridd), G Llewellyn (Neath), S Williams (Northampton), V Cooper (Llanelli), G Thomas (Bath), R Parks (Pontypridd), M Williams (Cardiff), D Jones (Llanelli), C Charvis (Swansea, capt), M Owen (Pontypridd)