The craft was flying a manned test over a California desert when the tragedy occured.
Virgin Group founder Richard Branson tweeted: "Thoughts with all @virgingalactic & Scaled, thanks for all your messages of support." He added that he was flying out to "be with the team".
The news represents a major setback to Branson’s long-held hopes of pioneering a new industry of space tourism. Speaking in October, Branson had said he intended the craft to make it to sub-orbital space within a matter of months.
In a statement today, Virgin Galactic said the craft had been flying a manned test when the "vehicle suffered a serious anomaly resulting in the loss of SpaceShipTwo".
SpaceShipTwo is designed to be carried by a jet, before being launched into sub-orbit. The company said the aircraft which held the spaceship had landed safely.
Thoughts with all @virgingalactic & Scaled, thanks for all your messages of support. I'm flying to Mojave immediately to be with the team.— Richard Branson (@richardbranson) October 31, 2014