Musk was elated, tweeting "Mars, here we come!!"
The explosion comes after first high-altitude test flight of the futuristic Starship earlier this week was aborted at the last second.
An automatic engine abort occurred with just 1.3 seconds remaining in the countdown.
SpaceX already has conducted five Starship test flights, but these earlier, simpler models have gone no higher than 150 metres.
SpaceX has taken over Boca Chica in the far southeastern corner of Texas, near the Mexican border, to build and test its Starships. The company intends to use Starships — the upper stage atop Super Heavy boosters — to deliver massive satellites into orbit around Earth, and send people and cargo to the moon and Mars.
Additional reporting, AP
