Konta, winner of the weekend’s Miami Open, would have been the number two seed in the WTA event.
“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.