The aircraft suffered "substantial damage", a spokesman for the Federal Aviation Authority said.
It was in the Grand Canyon West area when it came down at around 17:20 local time (00:20 GMT) on Saturday.
It is not yet clear what caused the crash, or which company operated the helicopter.
Local media said the helicopter was an Airbus Eurocopter EC130.
The Grand Canyon, which is more than 1.6km (one mile) deep, is one of the most visited tourist attractions in the US.
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