The incident happened at about 1.55am in the South Terminal. The man was challenged by officers, who used a taser to subdue him. The incident is not being treated as terror-related.
A 30-year-old man from Crawley, who was not a travelling passenger, has been arrested on suspicion of possessing offensive weapons and making threats to kill.
He currently remains in police custody.
Superintendent Justin Burtenshaw said: “Officers at Gatwick are there to keep passengers and staff safe. This incident was dealt with swiftly and no members of the public or police were harmed.”
Anyone with information, or who witnessed the incident, should call Sussex Police on 101, quoting serial 0089 of 03/06, or provide any details online through the Sussex Police website.