Orangeburg County Sheriff Larry Williams told several media outlets the children were recovered from the North Edisto River after the car as found near a boat landing Monday.
Williams told WIS-TV the child's mother has been charged with leaving the scene of an accident.
Neither the names of the victims nor the mother were immediately released. Williams did not immediately return a phone call Monday afternoon. Authorities were alerted early Monday about the car but have not said how the vehicle ended up in the water.
Divers recovered the bodies of the children about 45 minutes after they were called to the scene.