Morgan, who was World Cup co-captain with Dewi Lake last year, missed this year's Six Nations because of a knee injury.
But he now has a hamstring problem that he suffered during Ospreys' United Rugby Championship quarter-final defeat against Munster earlier this month.
The Welsh Rugby Union announced on Tuesday that Morgan has been released from the squad, meaning he misses the weekend match against the world champions and Tests in Australia on July 6 and 13.
Lake will skipper Warren Gatland's team against South Africa.
Cardiff scrum-half Ellis Bevan will make his senior international debut while Eddie James, James Ratti and Jacob Beetham could win their first caps from the replacements' bench.
Cardiff flanker James Botham, the grandson of England cricket great Ian Botham, starts in the back row alongside Taine Plumtree and Aaron Wainwright even though he was only called up on Monday.
There is a recall for Liam Williams, who will play on the wing. Williams missed the Six Nations due to club commitments after signing for Japanese club Kubota Spears.
Wales are without their England-based players including Nick Tompkins, Dafydd Jenkins and Tommy Reffell, because the game falls outside World Rugby's Test window.
South Africa are the "home" team on Saturday, with Twickenham their choice of venue, and Wales go into the game following six successive Test defeats.
"We have our backs to the wall a little bit this week, but we're really excited about the challenge on Saturday," said Wales coach Gatland.
"Facing the world champions at Twickenham Stadium will be a great occasion and we're relishing the opportunity to get out there and put in a performance."
Wales team to face South Africa at Twickenham
Team (15-1)
Cameron Winnett; Liam Williams, Owen Watkin, Mason Grady, Rio Dyer; Sam Costelow, Ellis Bevan; Aaron Wainwright, James Botham, Taine Plumtree; Ben Carter, Matthew Screech; Henry Thomas, Dewi Lake (capt), Gareth Thomas
Replacements: Evan Lloyd, Kemsley Mathias, Keiron Keiron Assiratti, James Ratti, Mackenzie Martin, Gareth Davies, Eddie James, Jacob Beetham
Coach: Warren Gatland (NZL)
