"The Office for the Protection of the Constitution (BfV) has managed to expose a suspected Islamist among its associates," the agency said in a statement, confirming information published earlier by the Der Spiegel weekly and the daily Die Welt.
The 51-year-old German, who was arrested for sharing "sensitive information" online, is believed to have been planning a bombing at the BfV headquarters in the western city of Cologne, according to the German press.
There was no immediate suggestion he had any ties to the radical Islamic State group.
Contacted by AFP, a BfV spokeswoman said the unnamed 51-year-old had "made Islamist remarks online under a false name, and had offered internal information during online chats".
She confirmed that an arrest warrant was issued and the suspect had been detained.
She did not though confirm the reports that he was plotting an attack, saying there was no "evidence of a real danger to the office or its workers".
Prosecutors are readying a case of "preparing a serious act threatening state security".
Both Der Spiegel and Die Welt said he had converted to Islam in 2014. Married with children, he was employed at a bank and had, since April, also been doing some work for the agency gathering intelligence on the Islamist scene in Germany.
The publications said the suspect had partially admitted to the allegations by making references to bomb attacks carried out "in the name of Allah".
He used several different names online and allegedly divulged information about the agency in chat rooms, the reports said. His activities were uncovered about a month ago.
Germany has so far been spared the kind of large-scale deadly jihadist atrocities which have been carried out in Paris and Brussels, though individuals have carried out attacks and others have been prevented.