Loose forward Jones underwent a scan on Monday after leaving the field in obvious pain during the match at Murrayfield on Saturday and his arm was in a sling as the team boarded their flight from Edinburgh.
"Ryan is not going to be available," Wales assistant coach Robin McBryde said. "He has broken a bone in his shoulder. It looks as though he will be out for six to eight weeks."
Jones confirmed the bad news on his Twitter feed.
"So, so disappointed not to be involved Saturday but thanks for all your messages," he said.
Wales, last year's grand slam champions, will retain the title if they win by at least eight points, or seven so long as England do not outscore them by three tries.
Sam Warburton, captain of the grand slam side, is the obvious candidate to take over from Jones after winning the man-of-the-match award against Scotland. British and Irish Lions lock Alun Wyn Jones, who has returned to the side after injury, is another possibility.
Warburton missed the second round win against France through injury and started on the bench in the subsequent victory over Italy. McBryde said a decision about the captaincy would be made on Thursday.
Wales could select two specialist opensides with Justin Tipuric partnering Warburton. Tipuric started against Italy ahead of Warburton and took over from Jones at blindside flanker against Scotland.
"I thought Sam and Justin worked very well together in Scotland," said Wales defence coach Shaun Edwards. "Sam got a couple of turnovers after Tips had done the chop tackle beforehand.
"They worked in combination and that is what you need your back row to do, one will chop and the other get on the ball."
McBryde said Aaron Shingler or Andrew Coombes were other options on the blindside.
Lions loosehead prop Gethin Jenkins, who missed the trip to Edinburgh with a calf strain, has returned to training and will contest the starting position with Paul James.
Scotland lock Richie Gray, a leading candidate for the Lions tour of Australia this year, will miss the trip to France for the final weekend of the championship after tearing a hamstring against Wales.
Gray was stretchered off the field and Scotland doctor James Robson said he would be out of action for eight weeks.
Ireland fly-half Jonathan Sexton and wing Craig Gilroy have been passed fit to play in Saturday's other match against Italy but both centres Brian O'Driscoll and Luke Marshall are doubtful because of concussions sustained against France last weekend.
Sexton missed the games against Scotland and France because of a hamstring injury and Gilroy was unable to play against France because of a groin strain.
Scrum-half Eoin Reddan has undergone surgery after breaking a leg in the France match and right wing Fergus McFadden will be out of action for at least three weeks after fracturing a rib.
Ireland, who started the tournament by beating Wales in Cardiff before suffering two losses and a draw, have had 15 players either injured or suspended over the course of their campaign.