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The selectors have yet to decide on his replacement for the series decider, a Cricket South Africa statement said on Friday.
"Smith has been given a period of rest and rehabilitation on chronic left ankle injury," it added.
South Africa and Pakistan are level at 2-2 in the five-match ODI series, which serves as a warm-up for the Champions Trophy in England in June.
(Reporting by Mark Gleeson; Editing by Mark Meadows)