Passenger Phil Lobel said he saw someone bring a fire extinguisher to the cockpit during the incident and other passengers later showed him pictures they took of flames in the cockpit.
United Airlines spokesman Mike Trevino said the plane took off from New York's John F. Kennedy International Airport and was diverted to Dulles, where it landed at 9:36 p.m. All 105 passengers and seven crew members got off safely, Trevino said. He did not have any other details.
Baker said the FAA was investigating the fire but to her knowledge, there was no criminal activity involved.
The National Transportation Safety Board spokesman Keith Holloway said Monday the board has assigned three people to investigate the case. He said they will be examining the cockpit to determine the cause of the fire.
Lobel, who has a public relations business in Los Angeles, told The Associated Press that about 30 minutes into the flight he detected an electrical burning smell.
He said flight attendants began going over emergency instructions with passengers in the exit rows and someone brought up a fire extinguisher from the back of the plane.
Lobel said the plane landed within about 20 minutes and a half-dozen or more emergency vehicles met the aircraft in Virginia.
Sources say Ashley Olsen was one of the passengers on the plane.
About an hour after the plane landed, Lobel received an e-mail from United apologizing for the "experience" he had on the flight.