Ballance was struck on the gloves by a Morne Morkel delivery on the fourth and final day of the second Test at Trent Bridge, a match the hosts lost by 340 runs with the four-match series now level at one-all.
The left-handed Ballance has a torrid time with the bat in the first two Tests – with scores of 27, 4, 20, 34 – and his place in the team for the rest of the series was not secure anyway.
Surrey batsman Mark Stoneman is set to be added to the England squad that is likely to be announced on Thursday or Friday.
The left-handed Stoneman, who can bat anywhere in the top three, has scored three centuries in the County Championship this season at an average of 58.53 and also scored two half-centuries for the England Lions against South Africa A earlier this season.
Opening batsman Keaton Jennings is also under pressure to keep his place for the third Test but with Ballance already ruled out the England selectors will be reluctant to change two of the top three positions in the batting order.