The 30-year-old British and Irish Lions Test hooker is expected to miss the rest of this season after undergoing shoulder surgery on Friday.
His regional team the Ospreys say it is "unlikely" Hibbard will play again between now and the end of the campaign.
And it looks set to make him a major doubt for Wales' two Tests against the Springboks, in Durban on June 14 and Nelspruit seven days later.
Wales head coach Warren Gatland has already lost Hibbard's fellow Lions Sam Warburton and Leigh Halfpenny from his summer plans.
Both Warburton and Halfpenny suffered dislocated shoulders during the RBS 6 Nations Championship - flanker Warburton in the dying seconds of the final game against Scotland, and full-back Halfpenny six days earlier when Wales were beaten 29-18 by England at Twickenham.
Ken Owens, who started in the number two shirt against Scotland when Hibbard was on the bench, would be a firm favourite to continue in that role against South Africa, with his Scarlets colleague Emyr Phillips providing main back-up.
Hibbard, who will join Aviva Premiership club Gloucester at the end of this term, appears to have played his last game for the Swansea-based Ospreys.
Ospreys medical performance manager Chris Towers said on Friday: " Richard has an ongoing shoulder problem that has been troubling him, and after returning to the region this week he feels unable to continue playing.
"It is in his best interests to get this issue resolved, and he will undergo surgery today.
"The expected minimum recovery time for such a procedure means it is unlikely he will play again between now and the end of the season."
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- Leigh Halfpenny
- Sam Warburton