"I was battling a slight shoulder injury and sickness during Miami which has taken hold," Konta said in a statement.
Konta, the world number seven, won the biggest title of her career when she beat Caroline Wozniacki 6-4 6-3 in the Miami final on Saturday.
American Madison Keys is the Charleston event's top seed.
(Reporting by Gene Cherry in Salvo, North Carolina, editing by Pritha Sarkar)
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