The sequence, created by Lucasfilm's special effects team ILMxLAB, allows users to look in all directions as the camera whizzes through the sci-fi scene.
When watched on a normal computer, the mouse is used to move the view.
On mobile devices, a user can move the device around to alter the perspective. Other 360 videos posted include content from Discovery, GoPro, NBC and Vice.
Currently, this type of video requires a relatively complex filming set-up to achieve the 360 effect.
But as the technology improves, Facebook hopes it will become widespread among its users.
"In the future, imagine watching 360 videos of a friend's vacation to a small village in France or a festival in Brazil - you'll be able to look around and experience it as if you were there," the social network said.
"Along with updates from your friends and family, you will also be able to discover amazing new content on Facebook from media companies, organisations, and individual creators."
Virtual actors
The new feature coincided with Facebook's now annual Oculus Connect event - a developers conference for people creating virtual reality experiences and hardware.
They included using virtual environments to visualise how movie sets would look before they were built - including creating virtual representations of actors in the scene.
However, Mr Bredow was hesitant to suggest VR would be the future of movies, cautiously suggesting that current hardware was not "comfortable enough".
"I wonder if a 360-degree movie is going to be compelling enough as its own medium," he added. "We haven't solved all the things we need to solve."
Facebook bought Oculus VR, the company behind the Oculus Rift headset, for $2bn (£1.3bn) in March last year.
Eventually, it is expected that Facebook's 360 video will support the as-yet unreleased Rift headset, which would produce a more immersive experience than interacting with 360 video on a screen.
Fierce competition
Facebook's main rival in online video, YouTube, has already entered the 360 video space.
The company also faces fierce competition in the hardware market as well - the Oculus Rift is set to be released after the HTC Vive, a key competitor backed by games firm Valve.
Sony's Morpheus headset is also expected in 2016.