Smit made a favourable impression on Saturday in the 31-31 draw with the Barbarians at Wembley, scoring one of South Africa’s tries, and had been expected to get a first cap against England.
The Boks are without injured flankers as Marcell Coetzee, Siya Kolisi, Jaco Kriel and Francois Louw while veteran Schalk Burger and Heinrich Brussouw are also unavailable.
Smit will be replaced by Uzair Cassiem, captain of the Cheetahs.
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Utility back Jesse Kriel was ruled out after suffering a leg injury against the Barbarians and winger Bryan Habana is doubtful for the England game with a knee injury.
South Africa also play Italy in Florence on Nov. 19 and Wales in Cardiff on Nov. 26 on their European tour.
(Reporting by Mark Gleeson in Cape Town; Editing by Ed Osmond)
