Police believe an armed man, who breached the airport's security perimeter on Saturday night and drove his car onto the tarmac, is holding his daughter hostage in what appears to be a custody dispute.
A special police task force and police psychologist were at the scene and communicating with the man.
Hamburg Airport has been completely evacuated.
The man has a gun and fired it twice into the air, according to federal police spokesman Thomas Gerbert.
It was unclear whether there was a second child in the vehicle, as initially suspected.
The man's wife had previously contacted the state police about a possible child abduction, according to the police spokesman.
He said there is a heavy state and federal police presence on site, with units deployed close to the vehicle in question. They included the federal police's evidence and arrest unit.
"They are very robustly equipped," said Gerbert.
A spokesperson for the airport said 27 flights had been affected.
In October authorities closed the same airport due to an attack threat on a flight from Tehran to Hamburg.
In July, climate activists from the Last Generation group paralysed the airport for hours. Flight operations had to be suspended for security reasons. Thousands of passengers were affected.