Jenkins has aggravated the calf injury that saw him miss the opening round defeat to England, while Rees is still struggling with a groin injury.
Both players impressed for the Lions on the 2009 tour of South Africa, becoming a permanent fixture in the Test front row.
But Wales have yet to see the best of them since their return, with Jenkins having only come on as a replacement against Scotland last weekend and Rees not yet playing any part in the Six Nations.
No timescale has been set for the length of the recovery process for either player but the Welsh Rugby Union has confirmed that they will not be fit in time to face France.
"Matthew is progressing well and will continue his rehab in camp with Wales," said Wales physio Mark Davies.
"He will undergo exhaustive testing over the next few days which will give us a clearer idea of when he may be available, but we can confirm that the France game will come too soon for him.
"Gethin has been scanned since leaving the field against Scotland and, as we thought, he has aggravated the calf injury which kept him out against England. At this stage we are not putting a time limit on his recovery, but again we know he will not take the field against France."
Injury to Jenkins is likely to see Ospreys prop Paul James continue at loosehead for Wales, while the absence of Rees and fellow hooker Gareth Williams opens the door for Huw Bennett or the uncapped Ken Owens to wear the No2 shirt against the unbeaten French.