The Environment Agency has confirmed that the item was discovered by Team Van Oord staff this morning during the excavation of a World War Two hut base.
A spokesman said: "We have assessed the risk to the public as low as the fire brigade and police are on site, and the airport has been closed along with their access road, Cecil Pashley Way.
"The Navy Bomb Disposal team are due to arrive imminently."
An unexploded ordnance is not necessarily a bomb, the spokesman said, but could be a variety of things, such as bullets or grenades.
A Shoreham Airport spokesman said Cecil Pashley Way would be closed until midday while the device is being dealt with.
"The airport has made the joint decision to cease all flying until being given the all clear by the Ministry Of Defence’s bomb disposal team," the spokesman said.
It is possible that the device is a World War Two bomb, the spokesman added.
The contractors are working on part of the Environment Agency's Adur Tidal Walls project.
The works at the airport are in reach W7 of the project and are currently due to continue until mid-autumn.