Chief executive Robert Sinclair said some 100 flights in and out of the airport in east London would be stopped after the device was found at the George V Dock on Sunday.
The Metropolitan Police set up a 700ft exclusion zone on Sunday evening to ensure the device could be dealt with safely.
Following the discovery of a World War Two ordnance in King George V Dock as part of planned development works, a 214m exclusion zone has been implemented as a precaution by the Met Police. As a result, London City Airport is currently closed. (1/3)
— London City Airport (@LondonCityAir) February 11, 2018
All flights in and out of London City on Monday are cancelled and an exclusion zone is in place in the immediate area. I urge any passengers due to fly today not to come to the airport and to contact their airline for further information. (2/3)
— London City Airport (@LondonCityAir) February 12, 2018
Scotland Yard said the German shell is 1.5m long and weighs 500kg and is stuck in a bed of dense silt, making it harder to remove.
A Scotland Yard spokesperson said: “The operation to remove the ordnance is ongoing in partnership with our colleagues in the Royal Navy.
“The timing of removal is dependant on the tides, however, at this stage we estimate that the removal of the device from location will be completed by tomorrow morning.
“While every effort is being made to progress the operation as quickly as possible, it is important that all of the necessary steps and precautions are taken to ensure it is dealt with safely.”
People living inside the zone were evacuated from their homes overnight, and police said a number of road cordons have been put in place in Newham.
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Commuters attempting to get to work this morning are also facing delays after Docklands Light Railway services between Pontoon Dock and Woolwich Arsenal were suspended.
Mr Sinclair said: “All flights in and out of London City on Monday are cancelled and an exclusion zone is in place in the immediate area.
“I urge any passengers due to fly today not to come to the airport and to contact their airline for further information.
“I recognise this is causing inconvenience for our passengers, and in particular some of our local residents. The airport is cooperating fully with the Met Police and Royal Navy and working hard to safely remove the device and resolve the situation as quickly as possible.”
Specialist officers are working with the Royal Navy to remove the ordnance, the Metropolitan Police said.
❗No service between Pontoon Dock and Woolwich Arsenal at police request following the discovery of a WWII bomb near London City Airport. Replacement buses service btwn Woolwich Arsenal and North Greenwich also btwn Canning Town and King George V.
— Docklands Light Railway (@LondonDLR) February 12, 2018
A spokesman said on Sunday night: “At 10pm an operational decision was made with the Royal Navy to implement a 214-metre exclusion zone to ensure that the ordnance can be safely dealt with whilst limiting any risk to the public.”
London City Airport is the 14th busiest in the UK with 4,540,000 passengers in 2017, according to data from the Civil Aviation Authority.