Flight 1704, which took off from Sacramento, was supposed to land at Bob Hope Airport in Burbank but was diverted to LAX, a spokesperson for Southwest said in an email.
One man aboard the plane said the landing was high-speed and rough.
Paul Mitchell said the pilot announced that there was a problem with the flaps and that the plane circled the Burbank airport before landing at the longer international runway at LAX.
"We came into LAX so low and so fast it was eerie," said Mitchell, the vice president of Political Data Inc. and a self-described frequent flier. "We landed ... almost at full speed."
Once the plane landed, airline staff told passengers they would be flown back to Burbank, but most of the passengers got off the plane, said Mitchell, who was calling from a taxi.
"Everybody applauded once the plane landed," he said. "I think it was a great job by the pilot, but it was obviously a little scary as we were getting there, and it was incredibly fast and kind of a real shock the way that we came in on the landing."
Southwest said the aircraft "has been taken out of service for inspection and repairs" and that the airline was working with customers to get them to their destinations. No one was injured.