Influential lock Jones will not travel to South Africa with his team-mates on Sunday, with head coach Warren Gatland explaining that the best case scenario was that the 35-year-old might be fit for the first Test against the reigning world champion Springboks in Cape Town on July 24.
His place in the 37-man touring squad has now been taken by fellow Wales second row Adam Beard, while Josh Navidi has been called up to replace flanker Justin Tipuric, who also suffered a shoulder injury against Japan and has been ruled out of the tour.
Murray, 32, is a veteran of two previous Lions tours in 2013 and 2017, making five Test appearances. He also has 89 caps for Ireland.
He was selected to succeed Jones as captain over the likes of Wales hooker Ken Owens, Scotland full-back Stuart Hogg and England duo Owen Farrell and Maro Itoje.
“We’re all incredibly disappointed for Alun Wyn and Justin,” said Gatland. “The timing of these injuries seem particularly cruel given we fly to South Africa on Sunday, but unfortunately they’re part of the game.
“Alun Wyn will obviously be a big loss, both on and off the field, but will be ably replaced by Conor.
“Conor is an outstanding rugby player and is held in the highest regard with both the players and coaches. As a three-time Lions tourist, he knows what will be required as captain and I am certain he will lead the squad with excellence. He will also be well supported by an experienced leadership group.
“We plan for Adam and Josh to join up with the touring party before we depart for South Africa on Sunday evening.”
The Lions begin their truncated eight-match South Africa tour with a game against the Emirates Lions in Johannesburg next Saturday.
They then face the Sharks, Bulls, South Africa ‘A’ and Stormers before the three-Test series against the Springboks begins.