Tropical storm Hilary has inundated streets across Mexico's dry Baja California peninsula with deadly floodwaters, before moving over southern California, where it has swamped roads and downed trees.

On Sunday, concerns were raised that flash floods could strike in places as far north as the US state of Idaho, which rarely gets torrential rain.

Hilary, which forecasters say is the first tropical storm to hit southern California in 84 years, is bringing flash floods, mudslides, high winds, power outages and the potential for isolated tornadoes.

The storm made landfall along the Mexican coast in a sparsely populated area about 250 kilometres south of Ensenada on Sunday, then moved through mudslide-prone Tijuana, threatening the improvised homes that cling to hillsides just south of the US border.

At least 9 million people were under flash-flood watches and warnings as heavy rain fell across normally sunny southern California ahead of the brunt of the storm.

Desert areas were especially susceptible along with hillsides with wildfire burn scars, forecasters warned.

Mud and boulders spilled onto highways, water overwhelmed drainage systems and tree branches fell in neighbourhoods from San Diego to Los Angeles.

Dozens of cars were trapped in floodwaters in Palm Springs and surrounding desert communities across the Coachella Valley.

Crews pumped floodwaters out of the emergency room at Eisenhower Medical Center in Rancho Mirage.

The Los Angeles Unified School District, the United States' second-largest school system, said all campuses would be closed on Monday.

"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," Superintendent Alberto Carvalho said at a media briefing.

San Diego schools postponed the first day of classes from Monday to Tuesday.

Southern California got another surprise in the afternoon as an earthquake with a preliminary magnitude of 5.1 hit near Ojai, about 130km north-west of downtown Los Angeles, according to the US Geological Survey.

It was felt widely and was followed by smaller aftershocks. There were no immediate reports of major damage or injury, according to a dispatcher with the Ventura County Sheriff's Office.

Tropical storm Hilary could wallop other western US states with once-in-a-century rains, with a good chance of it becoming the wettest-known tropical cyclone to douse Nevada, Oregon and Idaho.

Hilary was expected to remain a tropical storm as it moved into central Nevada early on Monday before dissipating.

By Sunday evening, Hilary had moved over San Diego and was headed north into inland desert areas. About midday, it had maximum sustained winds of 97 kilometres per hour.

National Hurricane Center director Michael Brennan said that while Hilary had weakened from a category four hurricane, it was the water, not the wind, that people should watch out for most.

He said some areas could get as much rain in hours as they typically got in a year.

"You do not want to be out driving around, trying to cross flooded roads on vehicle or on foot," Mr Brennan said during a briefing from Miami.

Climate disasters across the US

Hilary is the latest major climate disaster to wreak havoc across the US, Canada and Mexico.

Hawaii's island of Maui is still reeling from a blaze that killed more than 100 people and ravaged the historic town of Lahaina, making it the deadliest US wildfire in more than a century.

Firefighters in Canada are battling that nation's worst fire season on record.