The craft was undergoing manned testing when it experienced what the company described as “a serious anomaly”.
Television images shot from a helicopter showed what appeared to be wreckage bearing the Virgin logo.
SpaceShipTwo is carried aloft by a jet, then launched into sub-orbit.
In a statement, Virgin Galactic said the “vehicle suffered a serious anomaly resulting in the loss of SpaceShipTwo”.
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.
Ken Brown, a photographer who witnessed the crash, told the Associated Press news agency the craft exploded after it was released from a plane that carries it to a high altitude.
That aircraft, known as White Knight 2, has landed safely, Virgin Galactic said.
Analysis: David Shukman, BBC science editor
Even as details emerge of what went wrong, this is clearly a massive setback to a company hoping to pioneer a new industry of space tourism. Confidence is everything and this will not encourage the long list of celebrity and millionaire customers waiting for their first flight.
An innovative design for a spacecraft combined with a new type of rocket motor to make the development challenge exceptionally hard. Despite an endless series of delays to its spacecraft, Virgin Galactic has over the years managed to maintain some very optimistic public relations and positive media coverage.
I interviewed Sir Richard Branson when he first announced the venture and his enthusiasm and determination were undoubted. But his most recent promises of launching the first passenger trip by the end of this year had already started to look unrealistic some months ago.
Today’s accident will delay plans even further. Space is never easy, and making it routine is even harder.
The firm, a vision of Virgin Group founder of Sir Richard Branson, has been a front-runner in the nascent space-tourism industry and its chief said earlier in October it expected to see the craft make it to sub-orbital space within a few months.
About 200 people have already signed up for trips on SpaceShipTwo which cost about $200,000 (£125,000) per person
Earlier in the week, an unmanned supply rocket called Antares exploded shortly after its launch from the US state of Virginia.
It was carrying supplies for the International Space Station.
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