The hurricane warning issued Wednesday morning covers an area in the Gulf of Tehuantepec from Puerto Angel to Barra de Tonala.
Barbara's maximum sustained winds have increased to near 65 mph (100 kph). The U.S. National Hurricane Center in Miami says the storm is expected to become a hurricane before it reaches land. But it's expected to start weakening after the center moves inland.
The storm is centered about 70 miles (115 kilometers) south of Salina Cruz, Mexico, and is moving northeast near 8 mph (13 kph).