Team manager Mohamed Mosajee said Amla, the world's top test batsman, would return home after the conclusion of the first test on Friday for the birth.
Mosajee said Amla would attempt to return to Dubai for the second test, which starts on October 23, but his presence was not guaranteed.
Amla scored 118 not out, almost half of South Africa's total of 245 for eight, on Monday. It was his 20th test century.
(Reporting by Mark Gleeson; Editing by John Mehaffey)
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