The casualties are believed to be the pilots of the spaceplane, though California Highway Patrol Officer Jesse Borne did not identify them.
The injured person has been airlifted to a local hospital, Borne said.
Virgin Galactic has planned for years to sell trips in which SpaceShipTwo transports passengers about 62 miles above Earth, the beginning of outer space, and lets them experience a few minutes of weightlessness before returning to ground.
News of the crash of SpaceShipTwo came just after 10 a.m. local time (11 a.m. MT).
“During the test, the vehicle suffered a serious anomaly resulting in the loss of the vehicle,” the company said in a statement.
“We will work closely with relevant authorities to determine the cause of this accident,” the company said on Twitter.
The incident occurred over the Mojave Desert shortly after SpaceShipTwo separated from WhiteKnightTwo, the vehicle designed to carry it aloft, the Federal Aviation Administration said in a statement.
Television footage from CNN affiliate KABC-TV in Los Angeles showed SpaceShipTwo in pieces in the Mojave Desert.
Virgin’s chief, Richard Branson, was reportedly en route to the Mojave, a person who works for him told CNN.
It’s unclear what the failure of the spaceplane will mean for the program.
Virgin Galactic planned to send paying customers on SpaceShipTwo as early as 2015.
With composite lightweight materials, “feathered” rudders capable of turning 90 degrees and a hybrid rocket engine, it as safe as modern technology can make it.
Details of Friday’s test flight plan were not immediately known.
But in previous test flights, SpaceShipTwo has been loaded on the jet-powered WhiteKnightTwo, which can take the spaceplane to about 50,000 feet.
At that altitude, SpaceShipTwo would then fire its RocketMotorTwo — a hybrid rocket engine powered by both solid and liquid fuel.
SpaceShipTwo would reach supersonic speeds on its way to its intended altitude of about 62 miles above the Earth.
At that point, people onboard would get about five minutes of weightlessness before the bonds of earth retract with 6 Gs of force.
The spaceplane would then glide back through the atmosphere to landing.
Friday’s is the second incident in a week involving the commercial space industry.
On Tuesday, an unmanned Antares rocket exploded just after takeoff off the coast of Virginia.
Controllers deliberately destroyed the craft after it became apparent there was a problem, a spokesman for Orbital Sciences Corporation said Thursday.
CNN’s Brooke Baldwin, Rosalina Nieves, Sonya Hamasaki, Shelby Lin Erdman and Todd Leopold contributed to this report.