Two of the four people hurt Monday on the Ninja coaster were taken to the hospital as a precaution, but all the injuries were minor, fire and park officials said.
"We were going across one turn and all of a sudden a loud noise happened," Jeremy Ead, one of the injured riders, told KCAL-TV. "I ducked down just in time. A hard branch hit me in the head. I was there bleeding from my head, which was a little worse than this," he said, pointing to a gash in his forehead.
The coaster hit the branch about 5:30 p.m. and stopped, said Michael Pittman, a Los Angeles County Fire Department dispatch supervisor. It was nearly three hours later before all 22 of the riders were rescued.
At least one of the cars, which are normally suspended beneath the track, was dangling at an angle, derailed at the front.
Firefighters and park maintenance workers in harnesses removed the riders one by one. The riders waited patiently as firefighters tried to reach them through a tangle of track and trees, some talking with each other and others resting with their eyes occasionally closed.
All were alert and communicated with park staff during the evacuation process, Six Flags said in a statement.
The park's website advertises that Ninja swoops through the trees to give riders a thrill.
"As you shoot down the snake-like steel track you'll grip the hillsides and blast through the trees swiftly, slicing through the landscape," the ride's online description says. "Ninja pivots with precision as you narrowly miss tagging land and water, whipping around at 55 miles per hour."
The ride would remain shut down while the accident was investigated, park spokeswoman Sue Carpenter said in a statement.
Six Flags Magic Mountain is in the Valencia area of Santa Clarita, about 25 miles north of Los Angeles.
The accident comes just over a week after dozens of people were stranded more than 200 feet up on a revolving tower at SeaWorld San Diego for hours. Authorities there said a power failure stalled the ride.
In July of 2013, a woman was ejected from a roller coaster at Six Flags Over Texas in Arlington and died. The death was ruled an accident, but her family has sued both Six Flags and the German company that built the coaster's trains, both of whom denied any wrongdoing.
In September 2012 at another Southern California amusement park, Knott's Berry Farm, riders were left dangling at 300 feet for more than three hours when its Windseeker ride broke down. No one was injured in that breakdown.