The trustees were appointed to the Feza media group, which owns Zaman, Today's Zaman and other publications.
The court on Friday accused Feza publications of spreading propaganda to destabilize the Turkish state, according to the Anadolu Agency.
The action appears to reflect an ongoing power struggle between Turkish President Recep Tayyip Erdogan and a former ally turned bitter critic, the U.S.-based cleric Fethullah Gulen.
Erdogan accuses Gulen and his followers of creating a "parallel state" -- a clandestine group of people in official positions in the judiciary, law enforcement and elsewhere in government who are dedicated to the ouster of Erdogan and his allies.
On the other hand, critics accuse Erdogan of authoritarianism, including by stifling dissent and quashing free speech.
Sevgi Akarcesme, editor-in-chief of Today's Zaman, the English-language sister paper of Zaman, called the court's action a violation of the constitution and a "politically motivated ... witch hunt." She said the paper was unable to publish Sunday's edition and its Internet service was cut off.
Abdullah Bozkurt, a journalist at Today's Zaman, tweeted that staff had lost access to email accounts.
"No explanation, no notification whatsoever," he wrote. "They're pulling plugs on everything."
Turkish Prime Minister Ahmet Davutoglu defended the action as a judicial -- not a political -- decision.
"A democratically elected government which gets its legitimacy from the people has the right to question the activities, whether they be economic or journalistic, of those who have openly acted to bring about a coup," he said. "Turkey will never go backwards from where it has come in terms of press freedom but no one has the right to become a vehicle of a parallel structure within the state."
Another Turkish state official said, "This is not about clamping down on the media or press freedom. We are in a struggle against a terrorist organization."
Move condemned by free press advocates
The action of the Istanbul court Friday drew quick condemnation.
"Today's move by the court paves the way to effectively strangle the remnants of critical journalism in Turkey," Joel Simon, executive director of the New York-based Committee to Protect Journalists, said Friday.
In a statement, the European Union called on Turkey "to respect and promote high democratic standards and practices, including freedom of the media."
"Free, diverse and independent media constitute one of the cornerstones of a democratic society by facilitating the free flow of information and ideas, and by ensuring transparency and accountability," the statement said.
U.S. State Department spokesman John Kirby, in a statement, urged Turkey to "uphold the universal democratic values enshrined in their own constitution, including freedom of speech and especially freedom of the press."
U.S. Ambassador John Bass tweeted, "Judicial process must be respected, yes - but so must the importance of free press and due process."
Anti-censorship protests took place in front of Today's Zaman headquarters on Friday, and televised video showed protesters clashing outside the building with police, who fired tear gas and used a water cannon to disperse the crowd.
The Turkish state official said the protesters had "gathered without permission" and were warned multiple times before police dispersed them.
In a related development, four Turkish businessmen were detained as part of an investigation into the "parallel state," local police said.
Boydak Holding Executive Board Chairman Haci Boydak and his younger brother, CEO Memduh Boydak, were accused of being members of, and providing financial support to, the "parallel state." Two other executives -- Murat Boydak and Erol Boydak -- also were accused of being members and financial supporters of the clandestine group.