There are unconfirmed reports of “unauthorised” people on the airfield.
The official reason for the closure has not yet been revealed by authorities.
Flights are being diverted to Bremen and Hanover or being held, while outbound planes are stuck on the tarmac.
One Brit passenger tweeted he had been stuck on a Flybe plane for around half an hour, waiting for it to take-off.
He said: “I’m on a Flybe plane, on the tarmac at Hamburg Airport.
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“Pilot is calm and just said staff are searching for ‘trespassers’.”
Other passengers reported free drinks being handed out on their flights as they anxiously waited.
The airport is Germany fifth largest, with more 16 million passengers travelling through it each year.
The Duke and Duchess of Cambridge are among the famous faces to use it.
They flew back to the UK from Hamburg Airport in July after their visit to Poland and Germany.
More to follow.