One woman was taken in for questioning
The chief of the state police gave no details of the man's age or nationality, but told a press conference that he had a job "connected to air transport" and had worked at an airport.
The man would face charges including membership of a terrorist organisation, murder and an attack on air traffic, said chief federal prosecutor Kay Nehm.
A statement from Mr Nehm's office said the goal of the network under investigation was to co-operate with like-minded groups to carry out violent acts and attack the United States.
"There is a suspicion that, since the beginning of this year, a group has been founded in Hamburg... with the aim of carrying out serious crimes together with other Islamic fundamentalist groups abroad, to attack the United States in a spectacular way through the destruction of symbolic buildings".
Florida connection
German police were tipped off by the FBI on Wednesday night and carried out raids on eight flats in the city.
The man who was arrested was seized during the raid and an undisclosed number of other people were detained, including a woman from one of the flats who is being questioned as a witness.
Three men who were on the passenger lists of the hijacked planes were registered as Hamburg residents.
Two of them, Mohammed Atta and Marwan Al-Shehhi, are reported to have lived in Florida from July 2000 to January 2001 where they attended flying school.
Electronics students
According to their registration documents, both men came from the United Arab Emirates. They were enrolled as students at the city's technical university taking courses in shipbuilding and electronics.
Hamburg's Interior Minister, Olaf Scholz, said the two men had lived legally in Germany.
"It is evident that they avoided doing anything that would bring them to the attention of police or the immigration authorities," he said.
They are believed to have lived at one of the addresses searched by police in Wednesday night's raids in the Harburg part of the city.
The flat has been empty since February this year and police found the rooms had been carefully cleaned though experts still hope to find traces of the two men.
Extremist's haven
BBC Berlin Correspondent Rob Broomby says Hamburg has long had a reputation for attracting Islamic extremists, with allegations that activists in the city had raised money for Osama Bin Laden.
The head of the Hamburg state department for the protection of the constitution, Reinhard Wagner, confirmed that the city has connections to the Saudi dissident Osama bin Laden.
Mr Wagner said that aides "who have a role in Bin Laden's logistics, possibly as intermediaries for contacts or accommodation," were based in the city.
However Mr Nehm said that the Hamburg network under federal investigation was not known to have links with Mr Bin Laden.
Bin Laden connection
Although agents of Osama Bin Laden have been arrested in Germany before.
In 1998, Mamdouh Mahmud Salim, who US officials say was Mr Bin Laden's finance chief, was arrested near Munich by Bavarian authorities acting on a US warrant and turned over to American authorities three months later.
In December, authorities in Frankfurt arrested four suspected terrorists with ties to Mr Bin Laden, seizing bomb-making materials and weapons.
And a fifth suspect was arrested in Germany in April.