The torrential downpour came as thunderstorms pounded the area, bringing severe flooding primarily to the northwest section of the city.
The intense storm dumped 3 inches of rain in 90 minutes in one area, overwhelming flood control channels. Officials said 2.3 inches of rain was recorded in 20 minutes in one spot.
"Our street was a river," said Ann Friary, owner of Northshore Learning tree, a day care center in the northwest part of Las Vegas.
"There was so much water, we couldn't see the sidewalks."
Mayor Oscar Goodman declared a local state of emergency from what he called a "100 year storm." Such a storm should naturally occur just once every 100 years.
Goodman urged people not to leave their homes and stay off the roads.
"Remain calm," Goodman said at a televised news conference. "Remain in place."
Rushing water closed southbound lanes of U.S. 95, though some northbound lanes of the highway that links Las Vegas and Reno remained open.
Dime-sized hail pelted Henderson in the southwest, while the Las Vegas Strip saw only sprinkles.
No injuries were reported.
A search and rescue helicopter had to pluck at least two people from the tops of their cars, and four firefighters were rescued from their fire engine that became trapped by a raging wall of water in northwest Las Vegas.
Water rushed over block walls into a nearby residential area, damaging homes and property.
Some 3,000 customers in the city's northwest briefly lost power, Nevada Power Co. officials said. Power was restored to all but about 300 within a few hours.
Las Vegas officials activated the city's emergency operation center.
The American Red Cross was making plans to open shelters, Goodman said, though the agency's facilities had some flooding.
Goodman praised emergency workers.
"I think there are some heroic actions taking place," he said.
Goodman said the storm packed more of a punch than one in July 1999 that flooded the Strip and prompted the city's last state of emergency.
That 100-year storm caused more than $20 million in damage to public property. Two people died, and dozens of mobile homes were washed away. Numerous motorists had to be rescued.
A flash flood warning and thunderstorm warning would extend into the evening, officials said.