Streams of lava have been seen running through woods and bubbling on to roads.
Extreme levels of dangerous sulphur dioxide gas have been detected in the area, the Civil Defense Agency said.
Kilauea is one of the world's most active volcanoes and the eruption follows a series of recent earthquakes.
"It sounds like a jet engine," resident Ikaika Marzo told the Honolulu Star-Advertiser. "It's going hard."
Community centres have been opened to provide shelter for evacuees.
Talmadge Mango, the civil defence administrator for Hawaii County, said that power lines had melted off their poles in one area.
"Seismic activity is still extremely high, so we feel that this might just be the beginning of things," he said.
Officials had been warning residents all week they should be prepared to evacuate as an eruption would give little warning.
A volcanic crater vent - known as Puu Oo - collapsed earlier this week, sending lava down the mountain's slopes towards populated areas.
Local resident Stephen Clapper said he had told his mother to pack a bag "just in case", and they wasted no time getting in the car to drive to safety after the eruption.
"My neighbour came running over and said, 'What's that awful noise?'" Mr Clapper told local channel Khon TV. "He said he had never heard a noise like it, and he's been here for 40 years."
Hawaii's Governor, David Ige, says he has activated military reservists from the National Guard to help evacuate thousands of people.
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