Warren Gatland will now look to name a replacement lock and a new tour captain.
Jonny Gray, the Scotland second row, could come into contention to fill the former role. The Exeter Chiefs man scored a try in the Gallagher Premiership final against Harlequins at Twickenham on Saturday.
The loss of Jones is a huge blow for the Lions who will fly to South Africa on Sunday for the eight-match tour.
The hugely experienced Welshman sustained the injury as he was being cleaned out of a ruck and his left arm looked limp as he was helped from the field.
“He dislocated his shoulder,” said Gatland, the Lions head coach. “It went back in easy but the prognosis of him being fit, the very, very best-case scenario is that he might be able to make the first Test.
“He’s going to go and get scanned but we’ve just had a chat and we’re going to have to replace him.
“Very disappointing but he’s been around rugby long enough. He’s going to be gutted, it is very disappointing for him, but it was one of those things you’ve got to put behind you and move on as quickly as you possibly can.”
The compressed nature of the tour makes it unlikely that Jones could join up later even if he was able to recover in time.
“[The decision] is pretty much made,” said Gatland. “I was speaking to the physios, and they’ve spoken to Alun Wyn. He understands that the very best-case scenario is that he may get back for the Tests but we need to pull someone and get them PCR tested and hopefully get them on the flight with us tomorrow.
“We’re discussing a couple of names at the moment with the coaches. We’ll make that call and also potentially who’s going to take over as tour captain as well.
“We’ve got a leadership group which is pretty experienced so it’s not something that urgently needs to be done, but we’re just aware of who potentially steps into that role.”
Jones’ Wales team-mate Tipuric also departed in the first half after suffering a shoulder injury and faces an anxious wait to see if he will be fit for the tour.
“He got a stinger in the shoulder so we’re just going to check with a scan to make sure there is no nerve damage,” said Gatland.
“If there was any nerve impingement or damage that could rule him out, but at the moment we’re pretty confident he’s going to be OK, that it is just a stinger in the shoulder.”
Given the costly injuries to Jones and Tipuric, it was no surprise that No.8 Jack Conan was removed from the fray with ten minutes remaining as a precautionary measure.
“Just before kick-off, Jack Conan’s hamstring was a little but tight and he did brilliantly to get through 70 minutes, and we made the decision to take him off an play with just 14 men for the last 10 minutes because it wasn’t worth losing, potentially, another player before we get on the plane,” said Gatland.