The US Geological Survey said the 6.6 magnitude quake hit at 7.07am (0307 AEST) near the island of Hawaii and was followed by at least 10 aftershocks, one a moderate 5.8 magnitude.
Governor Linda Lingle issue a disaster declaration for the entire state.
She said in a radio interview that there had been no reports of deaths from the temblors.
But local media reported widespread power outages and damage to structures, including Kona Community Hospital in Kona, which had to be evacuated. There was no power on the island of Oahu, which includes the capital city of Honolulu.
A local reporter told CNN that the Honolulu airport was packed with stranded travellers who were facing fetid bathrooms, no running water and long lines for hand searches of their luggage.
"There is some power here and there," said reporter Daryl Huff.
"There is power for the fans ... but there's not enough power to run the computers to check people in."
Extensive road damage on the island of Hawaii had made driving conditions dangerous and officials were calling on residents and tourists to stay inside. Local television broadcasts revealed pictures of mudslides and boulders strewn across highways.
All of the state's airports were closed to outbound traffic, but inbound planes were being allowed to land.
Damage 'consistent'
Don Blakeman, a USGS seismologist, said the damage reports were consistent with an earthquake of this size.
"I wouldn't expect anything catastrophic," he said. "But you never know about these things."
Stewart Koyangi at the Pacific Tsunami Warning Centre in Hawaii said "no tsunami is expected," from this quake, but that some areas had experienced strong shaking.
The epicentre was some 253 kilometres from Honolulu, at a depth of 38.9km.
US media reported extensive disruptions from the quake, including all of the island of Oahu.
"Because of the island-wide blackout, things have come to a standstill," Mahea Richardson, a Hawaii television reporter, told CNN.
A Hawaiian Telecom spokesman told local media that phone service was not interrupted but that high demand had disrupted service. He called on residents to stay off the phone except for emergencies.
Tsunami fears
Erik von Ancken, who was vacationing on the island of Hawaii with his fiancee, told CNN that the devastating 2004 tsunami that killed some 220,000 was the first thing that crossed his mind.
"It was a little bit nerve-wracking," he said, noting that the fish started jumping before he could feel the shakes.
"The guess was that this was an earthquake," he said, "The tsunami, that was everyone's first thought. People started running for higher ground."
Stephanie Landers, a nurse at Hawaii Community Hospital, on the big island, said the quakes shook supplies off the walls and knocked air conditioning units down.
"There was a whole lot of rocking and rolling," she said, "and lots of screaming." But, she said, they had turned on emergency power and that things were returning to normal.