One case involved 16 million euros ($23.56 million) worth of turbocompressors found by customs inspectors in Hamburg that investigators believe could be used in Iran's missile prgramme, the magazine reported.
The shipment apparently came from a Siemens AG office in Sweden and was bound for an Iranian customer, it said.
The other case centred on computers that the British navy discovered on a Chinese ship near Dubai and bound for an Iranian company. The magazine said German industrial group Siemens had originally sent the computers, which can be used to help run nuclear plants and other purposes, to an address in China.
The economy ministry in Berlin was not immediately available for comment on the story, while a Siemens spokesman did not immediately return a call seeking comment.
Spiegel had quoted a Siemens spokesman as saying: "Our business activities in Iran serve exclusively civilian purposes and are in line with international law."
Iran's nuclear programme has been a bone of contention with the West, which suspects it may aim to make bombs.
(Reporting by Michael Shields; Editing by Angus MacSwan)
