The storm is expected to become a hurricane later Sunday as it moves west-northwest for two more days, before turning toward west into the Pacific by Tuesday, forecasters said.
Barbara formed off the southwest coast of Mexico earlier Sunday.
Heavy rainfall totals of 2 to 4 inches (5 to 10 centimeters), with amounts of up to 6 inches (15 centimeters) in limited areas, are possible across portions of the Mexican states of Guerrero, Michoacan, Colima, and Jalisco through Monday. Th rainfall may lead to flooding and mudslides.
Swells affecting portions of the southwestern Mexico coast for the next few days can produce life-threatening surf and rip current conditions, the hurricane center said.