Hines has been in superb form so far this season and is being talked about as a possible Lions contender but missing the Six Nations would leave him little time to convince head coach Ian McGeechan of his worth before the final squad announcement in late April.
The Australian-born Perpignan star was badly missed by his country last weekend as the Welsh forward pack exerted their dominance in the Scottish capital.
Scotland coach Frank Hadden had initially expected to have the former Edinburgh man back in his starting line up for Saturday's trip to Paris but Hines has now definitely been ruled out of that encounter.
Fellow Lions prospect Euan Murray will also miss the clash with France after failing to recover from a rib injury that saw him sit out the 26-13 loss to Wales.
With debutant prop Geoff Cross and wing Simon Webster also among a long list of names carrying injury worries, Hadden has delayed naming his matchday squad until later today.