The Wales fullback sustained an ankle injury, the BBC reported.
Williams, who has won 62 caps and started all of Wales's World Cup games except one, is not expected to recover in time for their next match - either the final or third-place playoff.
Leigh Halfpenny is expected to replace the 28-year-old in the lineup against South Africa when Warren Gatland announces the team on Friday.
Wales are already without loose forward Josh Navidi, who injured his hamstring in their 20-19 quarter-final victory over France on Sunday, with winger Owen Lane called up as a replacement.
The Six Nations champions are also keeping a close watch on centre Jonathan Davies, who was ruled out of the quarterfinal clash with a recurrence of a knee injury which he had aggravated in the penultimate pool game against Fiji.
South Africa also suffered a big blow ahead of the semi-final when winger Cheslin Kolbe was ruled out of the game with injury.
The winner of Sunday's semifinal will meet either England or New Zealand in the November 2 World Cup final.
