The action came amid a continuing crackdown on journalists and press freedom in Turkey.
Deniz Yucel, who has both Turkish and German citizenship, was detained on Feb 14 following his reports about a hacker attack on the email account of Turkey's energy minister, the newspaper said.
Yucel was questioned by a prosecutor in Istanbul for more than 3 hours before a judge ordered him formally arrested pending the preparation of an indictment and a trial. Die Welt confirmed that he was ordered into custody.
The crackdown has included the closure of at least 100 news outlets in Turkey.
More From This Section
The private Dogan news agency said Yucel was questioned about an interview he conducted with Cemil Bayik, a commander of the outlawed Kurdistan Workers' Party, as well as about articles he had written on Turkey's policies toward Kurds.
The Die Welt journalist also was asked whether he had any links to the hacker collective RedHack, which obtained the energy minister's emails that were made available on WikiLeaks, Dogan reported.
Germany's foreign ministry said last week that Yucel's case was of "greatest importance" for Berlin and that it would do "everything in our power to support press freedom" in Turkey.