The Metropolitan Police said the airport closed at 10pm, as officers worked with the Royal Navy to remove the bomb.
A 214m exclusion zone was put in place on Sunday evening to ensure the device could be dealt with safely.
People inside the zone were evacuated from their homes overnight, and road cordons are in place in Newham.
Passengers were urged not to travel to the airport on Monday and advised to contact their airline.
Docklands Light Railway services between Pontoon Dock and Woolwich Arsenal have been suspended.
Specialist officers were working with the Royal Navy to remove the bomb, the Metropolitan Police said.
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.