The 19-year-old suffered the injury in the latter stages of Saturday's tie which was suspended due to darkness.
She was trailing 7-6 (9/7), 6-6 when play was halted having received on-court treatment for the injury.
Despite having Sunday to try and recover, Keys, who had won the Eastbourne warm-up event on the eve of Wimbledon, was unable to take her place on Court 12 for today's resumption.
Shvedova, the world number 65 from Kazakhstan, goes on to face either Germany's Sabine Lisicki, the runner-up in 2013, or Serbia's Ana Ivanovic for a place in the quarter-finals.
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