Officials described the storm as highly dangerous.
The Mexican authorities have declared a maximum alert for the region and have prepared shelters for up to 30,000 people around the tourist resort of Los Cabos.
US Marines have been placed on standby to help out.
Residents and businesses were preparing as Hurricane Odile raced towards the peninsula.
The National Hurricane Center said Odile was initially a category 4 hurricane, with winds of up to 135 mph, but it lost some strength and was expected to be a category 3 when it made landfall on Sunday night, September 14.
In the Los Cabos resort, the authorities warned people to stay off the beach, remain indoors and keep away from doors and windows.
Officials said electricity would be shut off in the area as the storm hit to avoid damage from power lines if they came down.
At least 26,000 foreign tourists and 4,000 Mexicans were in the region, local officials said, and those in areas at risk of flooding were being evacuated.
Luis Puente, the head of Mexico’s civil protection agency, told reporters that 164 shelters had been readied with a capacity for 30,000 people.
Storm experts said it was set to be the strongest hurricane to hit the southern tip of the peninsula since Kiko in 1989, which landed as a category 3.
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