The loss came as a surprise to many who have followed Musk's California-based company through more than a dozen successful launches, even as competitor Orbital Sciences lost one of its rockets in an explosion in October, and a Russian Progress supply ship was lost after liftoff in April.
"These things do happen, but this was not the best time for this to happen," said Marco Caceres, a rocket industry analyst with the Teal Group.
"The one thing you could count on over the past few years was that the Falcon 9 was going to perform and was going to perform well," he told AFP.
PHOTOS: Astronaut Guide: How to Train Your Dragon
"In the midst of all this other chaos in the launch industry this was like, the one stable point and now we don't have that," he told AFP.
Caceres said the accident forces SpaceX, which has a billion-dollar-plus contract with NASA for supplying the ISS but is also competing with Boeing to send astronauts there by 2017, to launch again quickly.
"The moment they launch again successfully, this accident starts to fade into history really quickly. The longer they wait to launch again, the more people start talking about, 'Maybe we were too overconfident about SpaceX,'" he said.
The Dragon cargo ship was carrying 4,000 pounds (1,800 kilograms) of gear to the space station, including a large parking space, known as an International Docking Adaptor, designed to make it easier for an array of commercial crew spacecraft to dock at the orbiting lab in the future.
"Very sorry to see @SpaceX launch failure. Serious ramifications for Space Station resupply. Good thing it's international," wrote Canadian astronaut Chris Hadfield on Twitter.
NASA administrator Charles Bolden said the US space agency was "disappointed" at the loss but that the space station has "sufficient supplies for the next several months."
ANALYSIS: SpaceX Drone Boats Named After Sci-Fi Legend's Spaceships
A Russian Progress supply ship is scheduled to launch July 3, followed in August by a Japanese HTV flight, Bolden said.
"Orbital ATK, our other commercial cargo partner, is moving ahead with plans for its next launch later this year."
Three men are currently living at the space station. Russian cosmonaut Mikhail Kornienko and American astronaut Scott Kelly began their year-long mission in orbit back in March.
"Sadly failed. Space is hard," Kelly said on Twitter, posting a picture of his view of the Florida coast from space.
Earlier Sunday, station commander, Russian cosmonaut Gennady Padalka, 57, set a new world record when he became the person who has officially spent the longest amount of cumulative time in space -- 804 days.
His career includes one trip to the Mir Space Station and four to the ISS.