The two journalists said they received emails on March 1 saying their requests to renew their press cards were denied. Foreign journalists in Turkey need press cards to be granted residency permits.
Speaking to The Associated Press shortly before their departure, Seibert said the rejection came as a surprise and no explanation was provided.
After working in Turkey for 22 years, "I'm forced now to leave the country today," he said.
"This is unprecedented," Seibert said. "It has never happened before that the Turkish government has actually actively, expressedly rejected press card applications."
Brase said ZDF would appeal in court. He called the rejection "an attempt to put pressure on international media" after Turkish news outlets already had been "silenced."
"I happen to be one of these examples with which they try to put pressure on the others as well," he said. "But I don't think that this is going to work. And in the end, I think it will cause more damage to Turkey than it will cause to my station or to myself."
Halil Gulbeyaz, a reporter for German TV channel NDR, also was refused a new press card. Dozens of foreign journalists are waiting for their credentials.
Turkish Treasury and Finance Minister Berat Albayrak said at the end of February that Turkey renews journalists' credentials periodically just like the United States and European countries.
Albayrak was speaking at a news conference that some foreign journalists without new press cards were barred from attending.
"Some have had their accreditations renewed. Some are here, comfortably and freely asking questions. The accreditations of others have not been renewed," he said. "Every country's press freedom functions according to its own rules."
ZDF's director, Thomas Bellut, said other ZDF employees in Istanbul whose permits were renewed would continue to report Turkey and called the decision to expel the station's correspondent incomprehensible.
"He provided factual and competent reports from Istanbul," Bellut said in a statement.
"Turkey is an important country for Germany, and we will continue to report without prejudice, factually and also critically from Turkey and about Turkey," he said.
German officials have criticized Turkey's recent refusal to accredit the country's journalists. Foreign Minister Heiko Mass said in an interview with Tagesspiegel that such actions were "not compatible with our understanding of press freedom."
The Foreign Ministry updated its travel advice late Saturday for Germans planning to go to Turkey, citing Turkey's treatment of foreign reporters.
"It can't be ruled out that the Turkish government will take further measures against representatives of German media as well as civil society organizations," the ministry said.
The German Foreign Ministry also cited Turkey's "arbitrary arrest" in recent years of German citizens suspected of links to banned groups, such as outlawed Kurdish militants and the network of a Turkish cleric who lives in the United States. Turkey accuses Muslim cleric Fethullah Gulen and his followers of being behind a 2016 coup attempt.
The detentions of two German-Turkish journalists - Deniz Yucel and Mesale Tolu of Germany's Die Welt newspaper - on terror-related charges led to a diplomatic crisis in 2017. Yucel was held for more than a year without being inducted and left Turkey after he was released. Tolu was allowed to leave in August.
The Committee to Protect Journalists says Turkey is the top jailer of journalists in the world, with at least 68 journalists behind bars. The Turkish government has said the detentions were not based on the journalists' work and most stand accused of terror-related offenses.
In its 2018 press freedom index, advocacy group Reporters Without Borders ranked Turkey 157th out of 180 countries. The majority of Turkish media is pro-government, owned by businesses close to President Recep Tayyip Erdogan. More than a hundred news outlets were shuttered through emergency decrees in the aftermath of the coup attempt.
Maas said Germany would continue to discuss the issue of press freedom with the Turkish government.
"We have a great interest in a functioning dialogue with Turkey, so that such critical questions can be discussed as well," he said.