Maharaj suffered the injury while scoring 51 in the second innings with the Proteas eventually going on to win the Test by 328 runs.
The left-arm spinner went past the 200-wicket milestone in Bulawayo, the first Proteas spinner achieve the landmark in Test cricket.
Senuran Muthusamy has been named as a replacement in the squad while Prenelan Subrayen was already with the team in Zimbabwe and could make his Test debut if selected.
Proteas head coach Shukri Conrad said: "This is part of Wiaan's journey where he is starting to take more responsibility in the side.
"He has captained in his youth days, I think it was for the South Africa U-19s.
"I think it will be a great opportunity for Wiaan to grow into becoming a leader in this group. He has got all the attributes and the more responsibilities I give him the better he reacts."
Other news from the Proteas camp is that fast bowler Lungi Ngidi, who was to join the squad ahead of the second Test, has been released to give the seamers who impressed in the first Test another opportunity to build on their performances.
The second and final Test of the series starts at the Queen's Sports Club in Bulawayo on Saturday.
South African off-spinner Prenelan Subrayen has been cleared to continue bowling in international cricket following an independent assessment of his bowling action by the International Cricket Council (ICC).
The Proteas will start their World Test Championship title defence with a two-match series in Pakistan next month as part of an all-format tour.
Former England seamer Stuart Broad has raised concerns over the mental and physical fatigue affecting the national white-ball side.
South Africa clinched a dramatic five-run victory over England at Lord's to secure the one-day international series with a game to spare.
