Morgan, who was Wales' World Cup co-captain with Dewi Lake last year, missed this season'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.
And the Welsh Rugby Union announced that Morgan has been released from the squad, meaning he misses the Springboks encounter and Tests in Australia on July 6 and 13.
Hooker Lake, who also sat out the Six Nations due to injury, will be captain against South Africa at Twickenham, with James Botham wearing the number seven shirt and lining up in a back-row that also includes Taine Plumtree and Aaron Wainwright.
Cardiff halfback Ellis Bevan is handed a Test debut, while Liam Williams makes a first Wales appearance since the 2023 World Cup alongside back-three colleagues Cameron Winnett and Rio Dyer.
Wales are without their England-based players - the likes of Nick Tompkins, Dafydd Jenkins and Tommy Reffell - because the game falls outside World Rugby's summer Test window and means they cannot be considered for selection.
Wales have been badly hit in the second-row department, with Six Nations skipper Jenkins and his Exeter colleague Christ Tshiunza both unavailable, Will Rowlands being rested and Adam Beard injured.
Matthew Screech and Ben Carter are the locks selected to start against the world champions. Screech, 31, made his only previous Wales appearance as a replacement against Argentina in 2021, while Carter was last involved during the World Cup warm-up Tests almost a year ago.
There are three uncapped players on the bench in Ospreys forward James Ratti, Scarlets centre Eddie James and Cardiff back Jacob Beetham.
Wales head coach Warren Gatland said: "We have our backs to the wall a little bit this week, but we are really excited about the challenge on Saturday.
"Facing the world champions at Twickenham Stadium will be a great occasion, and we are relishing the opportunity to get out there and put in a performance.
"We have a big week ahead of us with this young squad, but the coaches and I have been very happy with the effort that is going in.
"There's a huge amount of potential in this group, and the next five weeks will be extremely important for us in terms of wanting to develop this team."
Wales team: C Winnett (Cardiff); L Williams (Kubota Spears), O Watkin (Ospreys), M Grady (Cardiff), R Dyer (Dragons); S Costelow (Scarlets), E Bevan (Cardiff); G Thomas (Ospreys), D Lake (Ospreys, capt), H Thomas (Scarlets), M Screech (Dragons), B Carter (Dragons), T Plumtree (Scarlets), J Botham (Cardiff), A Wainwright (Dragons).
Replacements: E Lloyd (Cardiff), K Mathias (Scarlets), K Assiratti (Cardiff), J Ratti (Ospreys), M Martin (Cardiff), G Davies (Scarlets), E James (Scarlets), J Beetham (Cardiff).
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