The Sharks flank, who has 10 caps, had a scan on Monday after limping out of the domestic Currie Cup final against Western Province on Saturday.
No decision has been made on a replacement, South African Rugby said.
It is the latest blow among the loose forwards for coach Allister Coetzee, with regular skipper Warren Whiteley and Jaco Kriel also ruled out through injury.
Du Preez's twin brother Daniel, who is uncapped and plays at number eight, will tour with the Boks as they face Ireland on Nov. 11, and then France, Italy and Wales on consecutive Saturdays thereafter.
(Reporting By Nick Said; Editing by Christian Radnedge)
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