Prop Welsh, 25, who won his sole cap to date against Italy in the final game of this year's Six Nations, suffered a recurrence of a shoulder problem during training on Friday on Scotland's last day in Sydney before they fly to Fiji on Saturday.
Scotland team doctor James Robson said: "Jon has had problems with his shoulder and today during a relatively innocuous tackle technique exercise he sustained a shoulder subluxation, where the shoulder partially dislocated from the joint.
"We were able to put it back in but I believed it was appropriate care for Jon to be scanned and the scan showed that the shoulder had sustained damage incompatible with the demands of international rugby and sadly he will take no further part in the tour.
"He will be reassessed on return home with a view to possible surgery."
Scotland head coach Andy Robinson said: "We are all disappointed for Jon who has trained well and been a popular member of the squad. We wish him a speedy recovery.
"We are now making arrangements for Moray to fly out and he will join us in Fiji early next week."
Welsh's Glasgow Warriors clubmate Low, 27, who won the last of his 15 caps in the EMC Test against Italy last year, has fought back from injury this season to be part of the Glasgow squad that reached the semi-final play-offs of the RaboDirect PRO12.
Meanwhile, flanker Alasdair Strokosch returned to team training today following the head wound he sustained during the celebrations at the 9-6 victory over the Wallabies on Tuesday in Newcastle.
Back Joe Ansbro (head wound) did not train today but showed visible signs of improvement as the swelling receded around his eye.
Wing Sean Lamont (ribs) undertook a recovery session in the hotel swimming pool, while hooker Ross Ford did rehab running at the St Pius grounds.
Full-back Stuart Hogg also was rested from training today on account of mild tendonitis.
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