The airport, in West Sussex, said the evacuation was a precaution while it continued to investigate.
“Passengers will not be able to enter the South Terminal while this is ongoing,” the spokesperson said.
“We are working to resolve the issue as quickly as possible.”
National Rail said no services would be calling at Gatwick Airport while police dealt with the incident.
A Southern spokesperson advised passengers not to travel to Gatwick.
“At present, the station and airport are being evacuated whilst the police are dealing with an incident,” they said.
“We would recommend delaying your journey until later this morning.”
Thameslink, Southern and Gatwick Express services are affected.
