An AirTran Airways spokesman said there's no danger to flights in the air, and flights are still taking off and landing.
However, spokesman Christopher White said flight plans are having to be inputted manually because of a malfunction with the automated system.
"Everything is safe in the air," White said.
Hartsfield-Jackson Atlanta International Airport, the world's busiest airport, has been particularly affected.
AirTran had canceled 22 flights and dozens more flights were delayed as of 8 a.m. EST. Delta Air Lines also has been affected.
The FAA said in a statement that it is having a problem processing flight plan information.
"We are investigating the cause of the problem," the agency said. "We are processing flight plans manually and expect some delays. We have radar coverage and communications with planes."
Passengers are being asked to check the status of their flights online before going to airports.