Officials say the fire has burned roughly 250 acres so far.
A portion of a highway north of Conway has closed because of low visibility and the need to move fire equipment.
Conway is about 15 miles northwest of Myrtle Beach.
The eastern half of the state is under a red-flag fire warning, with winds gusting up to 30 miles-per-hour and low humidity. The ground also is dry, which creates dangerous wildfire conditions.