The US diplomat “was asked to help in the swift clarification” of the case, the foreign ministry said.
German officials confirmed the arrest but released no other details.
US-German ties were strained after allegations last year that the NSA bugged Chancellor Angela Merkel’s phone as part of a huge surveillance program.
The scale of the agency’s global spy program was revealed in documents leaked by Edward Snowden.
The revelations also raised feeling in Germany against American surveillance.
German media say the man arrested this week is a 31-year-old employee of the federal intelligence service, the BND or Bundesnachrichtendienst.
A spokesman for 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 news agency 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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