Firefighters said construction debris in an elevator shaft apparently was ignited by a welder. Fire crews were sent to the terminal at shortly after 8:30 a.m.
Officials said the fire was out in about 15 minutes, but smoke lingered in the terminal.
Many passengers and employees were evacuated to a baggage claim area at the terminal. It was unclear if they were rescreened by security agents before being allowed to board flights. Fire officials said TSA agents were able to resume normal operations just after 9 a.m.
Terminal 6 is used by Allegiant, Continental, Frontier, Great Lakes and some United flights, according to Los Angeles World Airports data.
City News Service contributed to this report.