Cowan-Dickie, who came off the bench for first-choice Jamie George, has a tight hamstring following England's thrilling 42-39 loss to the Springboks at Ellis Park on Saturday, according to officials.
Singleton, 22, could earn his first England cap, but did feature for the side in their 63-45 loss to the Barbarians at Twickenham last month.
The tourists are seeking to snap a four-game losing streak in the second match of the three-test series against the Boks at the weekend.
The final match will be played in Cape Town on June 23.
(Reporting by Nick Said; Editing by Mark Heinrich)
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