Police Scotland said the terminal and access road had been closed following the discovery of "a potentially suspicious bag" in the central search area of the airport.
Passengers and staff were asked to leave the terminal building while an investigation takes place.
Edinburgh Airport said an investigation was under way and could not yet comment on whether flights had been affected.
A Police Scotland spokesman said: "Police at Edinburgh Airport have implemented a closure of the building and the access roads following the discovery of a potentially suspicious bag within the central search area at around 1.50pm today.
"The Explosive Ordnance Disposal are currently in attendance to inspect the item and officers are maintaining a cordon to ensure the safety of the public."