The incident happened at 9.05am local time (6.30pm GMT) when the aircraft was forced into its emergency stop system.
There are no reported injuries.
The Federal Aviation Administration (FAA) said in a statement: “Shortly after 9:05am PT today, @SouthwestAir Flight 278 rolled off the end of Runway 8 while landing at @fly_BUR Airport in #Burbank, CA, and came to rest in the Engineered Material Arresting System (EMAS). This information is preliminary and may change.”
The FAA added the airport remains open and that flights to and from Burbank are fully operational.
An image of the scene shows passengers being helped off the plane by fire fighters and officials in yellow high-vis jackets.
The plane itself lays on a crumbled runaway with its wheels buckled. Debris from the incident coats the lettering of the aircraft.
Another image from the side of the plane shows one of the wings severely damaged as a result of the crash.
Southwest Airlines says it is canceling all its flights at the airport until at least 1.55pm.
An ambulance is currently on the scene.
Emergency slides have also been deployed to help passengers off.
The plane was said to have landed during torrential rain.
It was was stopped by the Engineered Material Arresting System, designed to stop an aircraft that goes off the end of a runway.