An airlines spokesman said the problem involved a data outage in the Midwest, leaving the airline unable to check passengers in since 7:40 a.m. Workers were manually checking in passengers.
Alaska Airlines President and CEO Brad Tilden said there may be a partial solution by noon, and the problem may be fixed by 5 p.m.
"We're doing everything we can to get back on track," Tilden said.
The Seattle-based airline is the seventh largest in the U.S. and has an average of 436 flights a day at 64 destinations.
The problem did not cause any flight delays in Burbank, but two flights departing from LAX, for Miami and Dallas, were delayed.
The Associated Press contributed to this report.