Ted Stevens International Airport manager John Parrott said the terminal was evacuated shortly after midnight and reopened about 3 a.m., the Anchorage Daily News reported.
The FBI identified the passenger arrested by airport police as Peter Friesema, who Parrott said "made a statement about a bomb in a bag" while checking in for an Alaska Airlines flight.
Parrott told the newspaper the FBI interviewed Friesema and determined the threat "non-credible."
The incident affected about a half-dozen flights, Parrott said.
Hundreds of passengers -- many of whom were dressed in summer clothing from their warmer departure cities -- huddled in doorways to keep warm in the chilled Alaska air, the News said. Shuttles transported the passengers, a dozen at a time, to the North Terminal for warmth.
Police also set up a road block at the entrance to the airport, preventing cars from getting to the terminal to pick up arriving passengers.