The FAA partially shut down operations Saturday at midnight Eastern Time after lawmakers failed to agree on legislation to extend the agency's operating authority.
Flights will operate as scheduled, and air traffic controllers will stay on the job, but about 4,000 employees will be temporarily out of work.
Passengers could see a big savings on their airfares. Airlines will not be able to collect the federal tax normally included in the price of an airline ticket.
Airlines, alerted earlier this week that FAA authority could expire, have been making adjustments to their computer systems and websites so that at midnight, taxes would no longer be added to airfares, said the Air Transport Association.
Passengers who bought their tickets before the shutdown, but who travel during the shutdown, may wind up due a refund, Treasury Department spokeswoman Sandra Salstrom said.
This is because it's not clear whether the government can keep taxes for travel that takes place during a period when the government doesn't have authority to collect taxes, Salstrom said.
Also, it wasn't clear if passengers who buy tickets after midnight with no taxes included would wind up owing taxes if their travel took place after FAA's operating authority is restored, she said.
The IRS will likely issue guidance later to clarify the situation.
Long-term funding authority for the FAA expired in 2007. Unable to agree on new long-term funding legislation for the agency, Congress has kept the FAA operating through a series of 20 short-term extension bills. The extensions had been routine until this week.
The shutdown is having other fallouts. Construction projects at Los Angeles International Airport and other airports will come to a halt.
The Associated Press contributed to this story.