The storm was forecast to remain at sea, though heavy rainfall may cause localized flooding and mudslides on Mexico's western coast. Around 2 to 4 inches (5 to 10 centimeters) of rain are possible across portions of Guerrero, Michoacan, Colima, and Jalisco states through Monday.
Swells affecting portions of the southwestern Mexico coast for the next few days could produce life-threatening surf and rip current conditions, the hurricane center said.
Another tropical storm, Cosme, formed southwest of Barbara's position and was posing no threat to land.
Cosme had 45 mph (75 kph) maximum sustained winds late Sunday and may be near hurricane strength Monday, U.S. forecasters said. It was blowing to the northwest at 9 mph (15 kph) and was centered about 650 miles (1,045 kilometers) south-southwest of the southern tip of Baja California.