BfV head Hans-Georg Maassen said: "We have noticed that so many procurement activities have taken place from the embassy."
"From our point of view, they were for the missile programme but also partly for the nuclear programme," Maassen added in an interview with German public television channel ARD, to be aired on Monday.
Extracts of the interview were published on Saturday. Although the exact nature of the technology was not specified, the intelligence chief said they would have civilian and military uses.
"When we see such things, we stop them. But we cannot guarantee that we spot and block each attempt," he said.
Germany's domestic intelligence agency obtained clues on the technology procurements in 2016 and 2017, according to an investigation by ARD.
In 2014, it said a North Korean diplomat attempted to obtain equipment used in the development of chemical weapons.
The German accusations come after the publication on Friday of a United Nations report which says North Korea is flouting sanctions by exporting coal, iron, steel and other banned commodities, earning nearly $200 million in revenue last year.
A UN panel of experts also found evidence of military cooperation by North Korea to develop Syria's chemical weapons programmes and to provide Myanmar with ballistic missiles.