The Pacific Missile Range Facility said the aircraft crashed on the north side of the installation shortly after 10 a.m.
Information on casualties will be release when available, it said in a news release.
The helicopter was flying in support of a training operation, it said.
A Kauai County spokesperson said county police and firefighters responded and were assisting the military.
The Pacific Missile Range Facility is a Navy base on the western edge of Kauai where the military tests missile defenses and various units conduct exercises.