At 0900 GMT (local time) the centre of Kay was located some 495 kilometres southwest of the southern tip of the Baja California peninsula, the US National Hurricane Center (NHC) reported.
The storm, which was heading towards the northwest at a speed of six miles per hour, was packing maximum sustained winds of 50 miles per hour, the NHC said.
Even though the storm was not expected to make landfall, Mexican officials warned coastal communities to be on alert.
Kay could unleash "very strong focused storms in southern Baja California," Mexico's National Meterological Service said. It urged residents to "exercise caution."
Memory is still fresh of Hurricane Odile, which slammed Los Cabos on the southern tip of Baja California, in September 2014, killing six people and causing huge material damage.
Earlier in the month Tropical Storm Earl hit Mexico after weakening from a hurricane over Central America, bringing heavy rain and triggering floods along its path.
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