Jones is regarded as one of the best props in the world but will be unavailable to Wales until at least the final game of the competition against France.
The 31-year-old Ospreys front row damaged his elbow in the 24-12 Heineken Cup defeat to London Irish last weekend.
Ospresy physio Chris Towers said: "The scans have confirmed our suspicion of significant ligament damage and soft tissue trauma to the left elbow.
"We've discussed the case at length, both with orthopaedic specialists and the WRU medical team, and expect that Adam is likely to be out for around eight weeks."
As well as Jones and Jenkins, Gatland is also without centre Tom Shanklin and scrum-half Richie Rees with long-term injuries.
Meanwhile the returning Gavin Henson and Andrew Bishop are both extremely doubtful for the tournament opener against England on February 4 at the Millennium Stadium.