The rocket was launched at about 5.30pm (9pm GMT) in Los Angeles on Friday.
It successfully propelled 10 satellites into orbit an hour later.
The rocket first appeared as a red light which looked more like an unusual coloured star.
As it gathered height Californians were in awe as they saw a streak of light streaming across the clear sky at sunset.
Several celebrities joined fellow social media users in questioning what the mysterious light was.
Singers will.i.am and Billy Ray Cyrus asked what the streak was.
Skateboarding legend Tony Hawk, who was 120 miles south of LA in San Diego, asked: “What is this in the sky?”
Some users speculated that it was a UFO and aliens were coming to visit.
Musk, the multi-billionaire founder and lead designer at SpaceX, posted a video of the rocket in the sky and joked: “Nuclear alien UFO from North Korea.”
Danny Sullivan, Google’s public liaison for search, took a timelapse video of the rocket shooting over Southern California which garnered more than 30,000 views in half an hour.
Los Angeles Fire Department had to issue an alert explaining the “mysterious light in the sky” was the rocket launch.
The Falcon 9 rocket was launched from the Vandenberg Air Force Base for communications firm Iridium, which was part of one of the largest tech upgrades in history, SpaceX said.
Musk founded SpaceX in 2002 to “revolutionise space technology with the ultimate goal of enabling people to live on other planets”.
The company designs, manufactures and launches rockets and spacecraft.