The 70-foot (21 metre), two-stage Falcon 1 rocket was launched at 5.29pm (2229 GMT) from a US base on the Kwajalein Atoll in the Pacific Ocean's Marshall Islands on Friday.
The rocket lifted off from the launch pad but was destroyed about a minute later.
The rocket was designed and built by privately held Space Exploration Technologies, or SpaceX, of El Segundo, California.
Gwynne Shotwell, SpaceX vice president of business development, speaking to reporters on a teleconference call, said: "Clearly this is a setback, but we are in this for the long haul."
Musk, who sold his electronic payment service firm PalPay to Ebay for $1.5 billion in 2002, has high ambitions for SpaceX. He intends to cut the price of launch services with a family of semi-reusable rockets called the Falcon.
Even before its debut flight, SpaceX, which Musk founded four years ago, had won nine launch services contracts worth more than $200 million.
The cargo aboard the Falcon 1 rocket lost on Friday was a 43-pound (19.4kg), $750,000 department of defence satellite called FalconSat 2, which was to study how space plasma can disrupt communications and navigational positioning satellites.
The spacecraft was built by US Air Force Academy students and supported by the Defence Advanced Research Projects Agency.
SpaceX sells its smallest vehicle, the Falcon 1, for $6.7 million - about one-third the price of similarly sized rockets.
The Falcon 1 is a two-stage rocket powered by liquid oxygen and purified kerosene.
Musk, who has more than $100 million of his own funds into Falcon's development, has said repeatedly a launch failure would not be unexpected.
SpaceX has three more flights scheduled over the next 12 months and plans to debut its heavy-lift Falcon 9 in 2007.
It is among 20 companies competing for a commercial contract with Nasa to launch cargo to the International Space Station. Eventually, Nasa would like to hand over launches of its astronaut crews to a commercial carrier as well.
Friday's liftoff of Falcon 1 followed three unsuccessful attempts that were canceled due to technical issues.
In an earlier news conference, Musk said he figured his company could withstand one or two major launch failures, but a third disaster would probably put him out of business.
"I really feel that one successful launch will establish us as being fairly reliable," he said.