The force of the blast shook buildings several miles away.
SpaceX said "an anomaly" had occurred while the rocket was being loaded with fuel.
No one was injured, it said.
The rocket's payload, an Israeli-built communications satellite for Facebook due to launch on Saturday, was also destroyed, it added.
Facebook, in partnership with Eutelsat Communications, had been due to use the Amos-6 satellite to deliver broadband internet coverage for swathes of sub-Saharan Africa as part of its Internet.org initiative.
