At least two of those who died were children, according to reports in local media.
A search operation is under way for people who are still missing.
The flash flood occurred at Cold Springs, near Payson, on Saturday afternoon, sweeping people down East Verde River.
The Payson Fire Department said that multiple forest fires in recent months had created piles of debris that burst down a creek and through the swimming hole.
But it was not raining in the area where people were swimming.
At least four people have been rescued from the water and treated for hypothermia.
The National Weather Service has issued a flash flood alert for much of Arizona until Monday evening, with more storms expected in the middle of next week.

Investors remain optimistic that the election win for Prime Minister Shinzo Abe's party over the weekend will lead to more stimulus measures.
Mr Abe had described the vote as an endorsement of his reform policies and promised new government spending to help the economy.
Tokyo's Nikkei 225 index closed 0.8% higher at 16,231.43.
In China, Hong Kong's Hang Seng index ended the day up 97.63 points at 21,322.37 while the mainland Shanghai Composite closed up 11.31 points at 3,060.69.
Australia's benchmark ASX/200 index in Sydney rose 0.7% to close at 5,388.54.
With the iron ore price seeing a strong rise overnight, shares in commodity-related companies were among the best performers. Atlas Iron saw an 18% surge while Fortescue gained 6% and BHP Billiton was up just over 3%.
In South Korea, the Kospi closed up 0.7% at 2,005.55.
A deadly flash flood sparked by monsoon-like rains has swept through a swimming hole in the US state of Arizona, killing at least eight people.
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Japanese shares rose for a third day in row, leading a positive trend across the Asia Pacific region.