The UXB, believed to be a 500kg device, was found at George V Dock during planned work to the airport and has also forced some local residents to be evacuated.
According to the latest reports, specialists from the Metropolitan Police and the Royal Navy are on site and are currently attempting to remove it.
If they are successful, the only airport actually located in the city of London is expected to re-open for business on Tuesday.
A statement issued earlier today by the airport's CEO, Robert Sinclair, says: “The airport will remain closed for the rest of the day, following the discovery of a World War Two ordnance in King George V Dock on Sunday. An exclusion zone is in place in the immediate area.
"Any passengers due to fly today are urged not to come to the airport and to contact their airline for further information.
"I’m pleased to say some airlines were able to secure space at alternative airports so that some flights can operate – CityJet at Southend and Alitalia at Stansted. Thanks to those airports for stepping in to help out.
"I recognise this has caused inconvenience for our passengers, and in particular some of our local residents. The airport is cooperating fully with the Met Police, Royal Navy and London Borough of Newham to safely remove the device and resolve the situation as quickly as possible.
"The operation is proceeding well and we anticipate it to be completed during the course of this evening. At this stage we fully expect that the airport will be open as normal tomorrow.”
Passengers due to travel on Tuesday are asked not to arrive more than two hours before their flight.