Hilary made landfall around 250 kilometers (150 miles) south of the city of Ensenada before heading north towards Mexico’s second-largest city of Tijuana.
Across the border in the US state of California, at least nine million people were under flash-flood warnings.
“Catastrophic and life-threatening flooding likely over Baja California and portions of the southwestern US through Monday,” the US National Hurricane Center warned.
Residents across southern California spent the weekend filling sandbags and stocking up on supplies after Governor Gavin Newsom declared a state of emergency.
Hilary is the first tropical storm to hit the region in 84 years, and it is set to be the wettest on record.
Cities like Palm Springs are set to receive 6-10 inches (15-25 centimeters) of rain from the storm, compared to the 4.6 inches of rain Palm Springs usually receives an entire year.
“This is a dangerous storm,” said Zack Taylor, a meteorologist with the National Weather Service.
“It’s not just the rain totals but the intensity.”
Major League Baseball games in the areas have been relocated while hundreds of flights in and out of San Diego were also canceled.
California’s two largest school districts, in Los Angeles and San Diego, canceled classes on Monday, in a precautionary measure.
“There is no way we can compromise the safety of a single child or an employee, and our inability to survey buildings, our inability to determine access to schools makes it nearly impossible for us to open schools,” Alberto Carvalho, superintendent of the Los Angeles Unified School District, told a media briefing.
A 5.1 magnitude earthquake also struck north of Los Angeles as people hunkered down on Sunday afternoon.
Hilary brought flash floods and strong winds to Mexico over the weekend.
One person died on Saturday when their vehicle was swept away by water. The passengers were able to be rescued.
On Sunday, army troops used bulldozers and dump trucks to clear tons of boulders and dirt that clogged streets during the flash floods.