Hurricane heads towards Mexico's Baja California
Heavy rainfall was also expected in the southwestern United States from Friday as the storm moves north, the US National Hurricane Center (NHC) said.
At around 1500 GMT, Hilary was packing maximum sustained winds of about 85 miles (140 kilometers) an hour, according to the NHC.
The category one storm was located about 530 miles southeast of the tourist resort of Cabo San Lucas on the southern tip of Baja California, it said.
"Rapid strengthening is forecast during the next day or so, and Hilary could become a major hurricane," the NHC predicted.
"Flash flooding, locally significant, will be possible," it added.
The storm brought rain and rough seas to areas along Mexico's southwestern Pacific coast, including the tourist resort of Acapulco.
In the United States, parts of southern California and southern Nevada could see heavy rain through early next week, the NHC said.
Tropical cyclones hit Mexico every year on both its Pacific and Atlantic coasts, usually between May and November.