The Anadolu news agency said the warrants against the nationalist Sozcu newspaper's owner and three others were for committing crimes on behalf of the network of US-based cleric Fethullah Gulen but without being members.
The government blames Gulen for last summer's failed coup attempt, an allegation he denies.
Sozcu is a staunch supporter of the secular legacy of Turkey's founder Mustafa Kemal Ataturk and a sharp critic of Turkey's president and government.
Anadolu said the prosecutors are also investigating the four for "armed rebellion against the Turkish government" and "assassinating and assaulting the president", in reference to an article by Ulu on President Recep Tayyip Erdogan's location hours before the coup attempt.
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Sozcu's lawyer told reporters warrants for search and seizure at their homes were issued but not for detentions. The chief prosecutor in Istanbul, however, confirmed the investigation.
Kemal Kilicdaroglu, the leader of the main opposition Republican People's Party said the "operation" against Sozcu was "unacceptable" and called on the judiciary to act. "Turkey cannot take this pressure on the media," he said.
Lawyer Celal Ulgen called the decision "absurd, shocking" and insisted there could be no Gulen followers at Sozcu. He said the newspaper opposed the cleric.
Leading columnists at the paper protested the investigation. "This is what happens to the opposition in Turkey, this is what will happen to opposition newspapers but we won't give up and we won't be silent," said Emin Colasan, a senior journalist.
More than 47,000 people have been arrested for alleged links to groups Turkey lists as terror organisations, including Gulen's network. According to Platform 24, an independent watchdog, 165 journalists are behind bars in Turkey.