In a development likely to further strain bilateral ties, foreign ministry spokesman Martin Schäfer said Turkish authorities had failed to inform Berlin about the detention of the reporter, Mesale Tolu.
"That is regrettable," he said, adding that no German diplomats had managed to gain access to her since her arrest on April 30th.
"It is important to us that we can take care of her as a German citizen."
Schäfer said it was believed that Tolu - who according to media reports was born in Germany with Turkish citizenship but in 2007 became a German national - no longer holds a Turkish passport.
He said Turkish authorities were obligated to handle the case of Tolu, who is being held in a prison outside Istanbul, "not only with decency but according to international law".
"We will make this point loud and clear" to Turkey, Schäfer said.
German public broadcaster ARD reported on Thursday that a Turkish anti-terror police unit forcefully barged into the apartment of 33-year-old translator Mesale Tolu and arrested her. Friends told the broadcaster that the arrest had taken place in the middle of the night while she and her two-year-old son were sleeping.
Tolu has been working in Istanbul as a journalist and translator for a socialist-leaning news agency, as well as for a left-wing radio station, which was recently shut down by Turkish authorities. Her permanent address, though, is in Neu-Ulm, Bavaria, according to her brother.
She has been placed in a women's prison since May 6th, and a judge has reportedly issued a detention order against her for terrorist propaganda and membership in a terror organization.
Turkish news portal Diken reported that Tolu was arrested as part of a larger police raid in which 16 people were detained who also worked for her news agency or for left-wing political groups. The raid may have been planned ahead of May 1st protests, according to the report.
Schäfer said Tolu's young son was being cared for by her family.
Tolu's brother, Hüseyin Tolu, told broadcaster Radio 7 that the family has so far been denied contact with her.
"We are not allowed to see her, we are not allowed to visit her," the brother said, adding that he had traveled to Turkey to learn what happened to his sister.
"When we asked what the reason was [for the imprisonment], they said that it was still under investigation and they would not comment."
The brother noted that his sister's lawyer has so far been denied access to records. The lawyer has only been allowed to see her client three times since the arrest. The brother said that if even if his sister has in fact committed a crime, the family wants her to be transferred to the German justice system.
Schäfer said there were currently six German nationals in Turkish custody, four of whom also have Turkish citizenship.
The arrest is likely to only heighten tensions between Germany and Turkey, especially after another German-Turkish journalist was arrested and detained in February, also for terrorism-related accusations.
Die Welt correspondent Deniz Yücel is currently facing charges in Turkey of spreading terrorist propaganda and inciting hatred after he reported on emails acquired through a hacker attack against Turkish energy minister Berat Albayrak, who also is President Recep Tayyip Erdogan's son-in-law.
German Chancellor Angela Merkel has called the Turkish justice system's decision to detain Yücel “bitter and disappointing”.
Erdogan's ongoing crackdown and power grabs since an attempted coup by military members against him nearly a year ago has continued to result in conflicts with Germany and the European Union.
Amid campaigning for an ultimately successful referendum on April 16th to expand his presidential powers, the Turkish President accused German officials of using “Nazi measures” after a number of local authorities in Germany cancelled campaigning, citing security and logistical concerns.
In response, Merkel said her country could ban any future campaign events on its soil.
More recently, after Erdogan said he may consider holding another referendum to reinstate the death penalty - which Turkey abolished in 2004 in its ongoing bid to join the EU - Merkel said Germany would block Turkish citizens from voting inside Germany.
Turkey on Thursday also condemned Germany for reportedly granting asylum to Turkish military personnel with alleged links to the coup.