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 airport spokesperson said.
“We are working to resolve the issue as quickly as possible.”
Railway services are also not stopping at Gatwick Airport station until approximately 14:00 GMT, National Rail Enquiries said.
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.
Thameslink, Southern and Gatwick Express services are being affected.
National Highways said there were long delays from junction 9 of the M23 on the approach to Gatwick.