German daily Die Welt said its correspondent Deniz Yucel, 43, was detained on February 18 and his apartment searched in connection with news reports on an attack by hackers on the email account of Turkey's energy minister.
The minister, Berat Albayrak, is a son-in-law of President Recep Tayyip Erdogan.
In an interview published today by Die Welt, German foreign minister Sigmar Gabriel said it was "neither necessary nor just to deprive Deniz Yucel of his freedom for this long".
Under Turkey's state of emergency, Yucel can be held in police custody for up to 14 days without facing a judge, and prosecutors can then apply for him to be remanded in custody.
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"We continue to do all we can to find a solution," Gabriel added.
The foreign minister's statement come a day after 166 lawmakers in the Bundestag, the lower house of Germany's parliament, wrote an open letter to Turkish Ambassador Ali Kemal Aydin calling for Yucel's release.
According to a Die Welt statement at the time of Yucel's detention, the journalist reported on emails the leftist Turkish hacker collective RedHack had acquired from Albayrak's private email account.
"The emails concerned control of Turkish media groups and influencing the public by means of fake users on the messaging service Twitter," it added.
The paper says Yucel, who presented himself at the Istanbul police headquarters for questioning on February 14, is accused of "being a member of a terrorist organisation, misuse of data and terrorist propaganda".
Since that coup attempt, Turkey has clamped down on the press, arresting hundreds of journalists without trial.
About 170 media outlets have been closed and nearly 800 press cards cancelled, according to journalists' associations.