SpaceX said it would review data "to better understand [the] root cause" of the most recent explosion and noted it happened after the loss of "several" engines.
The Federal Aviation Administration (FAA) said the company would be required to conduct an investigation before it could fly again.
Nasa hopes to use a modified version of the spaceship as a human lunar lander for its Artemis missions to return to the Moon.
The tech billionaire has grand designs that the rocket system will one day take humans to the Moon, and then on to Mars, making humans "multi-planetary".
He said that the first Mars mission would carry the Tesla humanoid robot "Optimus", which was shown to the public last year.
Musk said the robot would one day be able to perform everyday tasks, and cost between $20,000 and $30,000.
On Friday, SpaceX launched its Falcon 9 rocket carrying a crew to the International Space Station (ISS) as part of a plan to bring two astronauts back home.
Butch Wilmore and Suni Williams were due to be on the ISS for only eight days, but because of technical issues with the experimental spacecraft they came on, which was built by Boeing, they have been there for more than nine months.
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