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Francis was carried off after taking a blow to his head during Saturday’s 32-29 first-Test defeat in Pretoria.
He faced a mandatory stand-down period of 12 days, but the Ospreys forward will now return home on Tuesday.
The Welsh Rugby Union said: “Tomas Francis will play no further part in the Wales tour in South Africa following the concussion he sustained in the first Test match against the Springboks at Loftus Versfeld.
“The WRU medical team have withdrawn Francis from the remainder of the series to allow him to optimise his recovery. He will return home to Wales tomorrow.
“Dillon Lewis, Sam Wainwright and Harri O’Connor are the remaining tighthead props in the squad.”
Wales head coach Wayne Pivac names his starting line-up on Thursday for the second Test, with one of uncapped pair Wainwright and O’Connor set for a bench place.
Saracens tighthead Wainwright was called into the tour squad as a replacement for the injured Leon Brown, while Scarlets forward O’Connor was added to the initial 33-player group just before the departure to South Africa.
Dewi Lake, meanwhile, has underlined Wales’ fierce belief that they can overturn a Test series deficit and make history in South Africa.
Wales face the Springboks in Bloemfontein next Saturday after seeing an 18-3 interval lead overhauled at Loftus Versfeld.
Hooker Lake’s late try hauled Wales level as they chased a first victory over the Springboks in South Africa at the 11th attempt.
But skipper Dan Biggar missed the conversion, before Springboks full-back Damian Willemse booted a match-winning penalty with the game’s final kick.
A gripping contest proved far closer than many had predicted, with Wales having arrived on tour following a Guinness Six Nations home defeat against Italy three months ago.
“We will have the bit between our teeth going into the next Test, and we will back ourselves to do it,” Lake told the Welsh Rugby Union official website.
“We have still got a chance to create history. We are only one down, and can still win it 2-1. It is not a case of it’s done for us and we are out of it.
An incredible, full-on Test match. Roll on the rest of the Series 🇿🇦 🏴 pic.twitter.com/PulSHgJs8j
— World Rugby (@WorldRugby) July 2, 2022
“The suggestion throughout the week was that we had no chance at all, but we have proved that one to be wrong already.
“We back ourselves to come out and do a job, and over the next two weeks it is up to us to do that. Bring on the next two weeks.
“We spoke about the toll it will take on us as a squad, both mentally and physically, for the past couple of weeks, but until you are actually in it you don’t get any feeling for it.”
The Wales squad will leave their Johannesburg base for Bloemfontein on Thursday, where two previous encounters against South Africa saw the tourists beaten 34-19 in 2002 and and 43-17 six years later.
We are here to put up a fight, and we are here to win games
And one area they must tighten is discipline after four Wales players – Biggar, Alun Wyn Jones, Louis Rees-Zammit and Rhys Carre – received yellow cards during the first Test.
Lake added: “When you are playing the best team in the world you can’t give away 15-17 penalties and four yellow cards because you just aren’t going to beat them.
“We have shown we are here to play. We are here to put up a fight, and we are here to win games. I am looking forward to the next couple of weeks.”