The gateway says the decision has been taken after speaking with police to ensure the safety and security of passengers and staff.
All incoming flights have been suspended and the approach road to the airport has also been closed, London Luton Airport adds.
A statement on the airport's website, continues: "Passengers are advised to contact their airlines to establish the status of their flights. Further updates regarding the security and operations at the airport will be provided as soon as possible."
The latest Twitter posting from the gateway reads: "We are working closely with the police to ensure minimum inconvenience, but we must ensure that the safety of all remains top priority."
