Authorities are searching for the missing after the incident on Saturday afternoon in the Verde River inside Tonto National Forest, about 145 kilometers northeast of Phoenix.
There was no warning before a wall of water hit the swimmers.
'They had no warning. They heard a roar, and it was on top of them,'' said Ron Sattelmaier, chief of the fire and medical district around Water Wheel Falls, Arizona.
Up to 4 centimeters of rain from an intense thunderstorm had fallen during one hour in a remote area about 14 kilometers upstream, local authorities said. The storm surge of water, swollen by debris from recent wildfires, reached a narrow canyon where people were taking refuge from the summer heat. The river burst its banks and overwhelmed the swimmers.
Unofficial reports said more than a hundred people may have been relaxing in the water at the time. Witnesses said survivors clung to trees as the water rose around them.
The severe thunderstorm that caused the sudden flood pounded down on an area charred by a recent wildfire, which left a deep burn scar on ground where pine trees, foliage and ground dust would normally absorb rain.
'If it's an intense burn, it creates a glaze on the surface that just repels water,'' said Darren McCollum, a meteorologist.
The National Weather Service had issued a specific flash-flood warning about an hour and a half before the tragedy in Tonto National Forest unfolded.
Most of Arizona is under flash flood watch until Monday evening, and the regional NWS center in Phoenix warned that 'heavy rains can produce flash flooding of low lying, normally dry areas such as washes.'