According to the US National Hurricane Center (NHC), Hurricane Newton could trigger flash floods.
The NHC warned that preparations to protect life and property “should be rushed to completion”.
On September 5, overcast skies in the Los Cabos municipality gave way to heavy rain and the wind was building in strength.
Twelve shelters opened and drivers queued to fill their cars with fuel ahead of the hurricane’s arrival.
The same weather system lashed areas of the south-western state of Guerrero over the weekend before strengthening to a tropical storm.
Torrential rain that began on September 3 caused more than 30 mudslides across Guerrero, forcing main roads to close.
In Acapulco, floods and landslides affected dozens of homes and schools and about 200 people had to be rescued from a housing complex.
Newton reached hurricane strength over the Pacific on September 5, prompting the Mexican government to issue a hurricane warning for the west coast of Baja California Sur from north of Puerto Cortes to Cabo San Lazaro.
The region is a popular tourist destination.
The NHC said that at 15:00 local time, the eye of the hurricane was about 215 miles south-east of Cabo San Lucas and grinding towards the coast at about 16mph.
It said that on its current path, Hurricane Newton should be near or over the southern end of the peninsula on Tuesday morning, September 6.
The NHC said it would move across the peninsula and reach north-western Mexico early on September 7.
Over the weekend, Florida was battered by Hurricane Hermine, before it weakened to a post-tropical storm and drifted off the US east coast.
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