Authorities were searching for at least one other missing person after the incident on Saturday afternoon in the Verde River near Payson, about 90 miles (145 km) northeast of Phoenix, Water Wheel Fire and Medical District Fire Chief Ron Sattelmaier said.
Local media reported at least two children were among the dead. The Gila County Sheriff's Office did not give details of the deceased or those missing.
A search-and-rescue operation was under way involving sheriff's deputies and the Arizona Department of Public Safety Ranger Helicopter, as well as members of the local Whispering Pines Fire Department and US Forest Service, Sheriff Adam Shepherd said in a statement.
The National Weather Service in Phoenix said that most of Arizona was under flash flood watch until Monday evening, warning that "heavy rains can produce flash flooding of low lying, normally dry areas such as washes."
(Reporting by David Schwartz; Additional reporting by Bernie Woodall in Fort Lauderdale, Florida; Editing by Frank McGurty and Sandra Maler)