The craft was flying a manned test when it experienced what the company described as “a serious anomaly”.
SpaceShipTwo is carried aloft by a jet, then launched into sub-orbit.
Virgin Group founder Sir Richard Branson tweeted he was flying to California “to be with the team”.
“Thoughts with all @virgingalactic & Scaled, thanks for all your messages of support,” Richard Branson said.
Television images shot from a helicopter showed what appeared to be wreckage bearing the Virgin logo.
In a statement, Virgin Galactic said the “vehicle suffered a serious anomaly resulting in the loss of SpaceShipTwo”. The aircraft that held the spaceship, known as White Knight 2, has landed safely, Virgin Galactic said.
Ken Brown, a photographer who witnessed the crash, said the craft exploded after it was released from a plane that carries it to a high altitude.
Kern County Sheriff’s spokesman told the Reuters news agency the craft’s co-pilot was killed, while the pilot ejected and was seriously injured.
Virgin Galactic has been a front-runner in the nascent space-tourism industry and Sir Richard said earlier in October he expected to see the craft make it to sub-orbital space within a few months.
More than 800 people have already paid or put down deposits for a trip on SpaceShipTwo, which costs about $200,000 per person.
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