A video of the incident recorded by a local space enthusiast captured the moment the top of the Starship MK-1 rocket exploded.
SpaceX said there were no injuries and that the incident in such an early-stage test of the rocket was not a serious setback.
“The purpose of today’s test was to pressurise systems to the max, so the outcome was not completely unexpected,” a spokesperson for the space firm said.
SpaceX CEO revealed on Twitter that tests would now proceed with the Starship MK-3 prototype design, which is more refined and features a much-improved flight design.
Mr Musk unveiled the Starship spacecraft in September, claiming it would be ready to carry humans to Mars within a few years.
“This is going to sound totally nuts, but I think we want to try to reach orbit in less than six months,” he said at the event in Texas.
The billionaire polymath also reiterated his belief that humanity needs to colonise the Moon, Mars and other parts of space in order to ensure its survival.
In order to achieve this, the company has ushered in a number of groundbreaking innovations to vastly reduce the cost of space travel, including reusable rockets that can land vertically following take off.
“We need to make space travel like air travel. Any other mode of transport is reusable so the critical breakthrough is a rapidly reusable orbital rocket – this is the holy grail of space,” he said.
"I think we should really do our best to become a multi-planet species, and we should do it now."