Arizona Gov. Jan Brewer declared a state of emergency Monday after unusually heavy rainfall flooded several major roads, triggered power outages and school closings in Phoenix, and caused one death.

A woman in her 50s was killed Monday morning when her car was swept away by rushing water in Tucson. Authorities hadn't identified her.

Phoenix Mayor Greg Stanton also declared a local state of emergency after the city saw record daily rainfall of more than 3 inches at Phoenix Sky Harbor International Airport. In an average monsoon season, which typically runs from July to September, the Phoenix area receives about 2.71 inches of rain. Maricopa and La Paz counties also declared states of emergency.

"I grew up here in Phoenix and I've never seen anything like it," Mr. Stanton said.

Rainfall in Tucson also broke records, reaching 1.87 inches by midday.

Ms. Brewer said the rains had damaged residential property and prompted evacuations, and she warned flooding could continue over the coming days. She called for $200,000 from the state's general fund to be made available to the Arizona Department of Emergency Management and authorized mobilization of the Arizona National Guard.

Flooding is common in Arizona. Several people drown in floodwaters annually in the mountainous desert state, according to the U.S. Geological Survey. But Arizona, which has more than 6.5 million residents, accounted for less than 50,000 flood-insurance policies in 2013, according to the National Flood Insurance Program.

The National Weather Service issued flash-flood warnings Monday for counties throughout Arizona, as well as parts of southern Nevada and California. Authorities encouraged Arizona residents to avoid several roadways and stay home Monday.

In Phoenix, as many as 10,000 homes were without power early Monday morning, but that fell to 250 by late morning, according to Arizona Public Service Co., the local power company.

Interstate 10 was flooded and inaccessible just west of downtown Phoenix on Monday morning, and emergency workers rescued several stranded drivers from the major freeway. Bart Graves, a spokesman for the Arizona Department of Public Safety, said at least a dozen cars were completely submerged.

The state Department of Transportation said pumps were working to clear water from the freeways, and progress would speed up as soon as the rain cleared.

Mr. Stanton said crews were working quickly to assess the damage around Phoenix, with a particular focus on the water delivery and drainage systems. "We're concerned about overflowing those systems," Mr. Stanton said. "They are full right now so we're monitoring them very closely."

Heavy rains also hit parts of Southern California overnight, closing several roads in parts of Riverside and San Bernardino counties, but no major damage was reported.

Write to Erica E. Phillips at erica.phillips@wsj.com

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