Nyakane had been named in the starting line-up for Saturday’s first test at Ellis Park in Johannesburg, which South Africa won 42-39, but pulled out before kickoff because of the injury and was replaced by Wilco Louw.
The size of the Springbok squad has also been reduced with Curwin Bosch, Nizaam Carr, Travis Ismaiel, Jason Jenkins, Ox Noche, Kwagga Smith and Cameron Wright released back to their clubs.
All but Carr and Wright played for the Springboks in their 22-20 loss to Wales in Washington DC on June 2.
South Africa's squad headed to Bloemfontein on Sunday, where the second test against England will be played on Saturday.
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(Reporting by Mark Gleeson; Editing by Pritha Sarkar)
