The man is said to have been trying to gather details about a German parliamentary committee that is investigating claims of US espionage.
German authorities have asked the US ambassador for “swift clarification”.
The NSA was last year accused of bugging the phone of German Chancellor Angela Merkel as part of a huge surveillance program.
The scale of the NSA’s global spy program was revealed in documents leaked last year by Edward Snowden.
The revelations about the NSA put a strain on ties between Germany and the US and raised feeling in Germany against American surveillance.
According to the German media, the man arrested this week is a 31-year-old employee of the federal service, the BND or Bundesnachrichtendienst.
The German federal prosecutor’s office confirmed the man’s arrest, but gave no other details.
A spokesman for Chancellor Angela Merkel said she had been informed of the arrest, as had the members of the nine-strong parliamentary committee investigating the activities of foreign intelligence agencies in Germany.
Der Spiegel news magazine said the man was believed to have passed secret documents to a US contact in exchange for money.
However, one unnamed politician told Reuters the suspect had offered his services to the US voluntarily.
“This was a man who had no direct contact with the investigative committee… He was not a top agent,” the source said.
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