It will be the first time an official four-day Test match is played and it will also be the first pink ball day/night Test in South Africa.
Du Plessis picked up a lower back injury during the third ODI against Bangladesh back in October and has not played since.
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It was initially expected that he would recover in time for the Zimbabwe Test, but he confirmed during an interview on Cape Talk on Tuesday that he was still unsure whether he would be able to take part in the match.
Should Du Plessis not feature, the logical captaincy options would be AB de Villiers and Dean Elgar, who captained the Proteas at Lord's this year in Du Plessis' absence.
If he does miss the Zimbabwe game, Du Plessis will certainly be looking to make his return for the India Test series, which gets under way in Cape Town on January 5, 2018.