The helicopter has an electronic locator, but no signals had been received, according to the Coast Guard.
The chopper was carrying a pilot and six passengers, two of whom were believed to be minors, the Coast Guard said.
Clouds and rain at the scene limited visibility to 6.4km, with winds at 45kmh. Friday's forecast predicted winds were at about 37kmh.
A rescue helicopter and crew was launched from Coast Guard Air Station Barbers Point, and additional support was provided by the Navy Helicopter Maritime Strike Squadron 37 at Kaneohe Bay. A Coast Guard cutter and crew were also launched from Honolulu.
"We're looking forward to first light when our visibility improves simply because we have daylight," Muir said.
Local fire officials planned to launch their own search efforts. Commercial helicopter companies and ATV crews were also being deployed.
Towering mountains and steep, deep ravines and cliffs line the coast.
"There are beaches along the Nā Pali coastline, but we are experiencing periods of very high water, so exactly how much beach may be available I couldn't tell you," Muir said.
Helicopter tours are common above the island of Kauai, much of which is made up of remote state parks.
- AP