The man, who is reportedly not in custody at this time, is believed to be held up near the rental-car area on the first floor of the airport.
The Orlando Police Department tweeted that there was no active shooter, and that no shots have been fired.
Roads leading up to the airport have been closed and the Florida Highway Patrol is reportedly telling people to stay away from the area.
According to a Reuters report, the airport serves about 42.6 million passengers a year and operates with 35 commercial airlines.
This is a developing story. Check back for updates.