Murat Sabuncu was arrested along with a dozen staff members in early morning raids on Monday.
The daily is known for its opposition to President Receip Tayiip Erdogan.
Last Spring it accused the government of seeking to illicitly deliver arms bound for Islamist rebels in Syria.
According to a statement from the Istanbul prosecutor, an investigation has been launched into allegations the paper's coverage "legitimised" an attempted coup last summer.
"Recently the newspaper has extended its editorial line," Erol Onderoglu, press-freedom campaign Reporters Without Borders representative in Turkey, told RFI. "It's more sensitive to human rights issues, kurdish issues. But all critical circles have been victims of crackdown from the judiciary. Today we can clearly say that media pluralism, critical voices have been extremely reduced in Turkey."
In total a dozen staff members were arrested and an arrest warrant was issued for the paper's former editor in chief Can Dundar, who was sentenced to a prison term in May and is now in exile in Europe.
Civil servants fired
The state of emergency declared after this year's coup attempt continues and this weekend Turkish authorities fired more than 10,000 civil servants and closed 15 other media outlets, most of them favourable to the country's Kurdish minority.
Critics say Erdogan is using the coup as an excuse to silent opposition voices.
"Things are getting worse and worse," says Tarık Günersel, a playwright and Secretary for PEN International in Turkey. "During the last few years, there was what I call a 'cold civil war', controlled to some extend. It's very frightening and very difficult."
A crowd of up to 70 people, including journalists and members of the main opposition Republican People's Party, gathered outside Cumhuriyet's headquarters in Istanbul on Monday.
"I think as a whole it's very hard for Turkish people to measure this importance such cases, because mainstream media are 80 percent under the control of the government," says Onderoglu, who attended the protest.
While the Turkish government insists it is acting within the law, organisations defending free speech have accused the government of violating human rights.
European parliament condemns crackdown
The European parliament recently passed a motion condemning the crackdown on free speech in Turkey but individual member states have been less vocal.
"It comes to this problem with refugees, some Western countries closed their eyes to Erdogan's despotic measures for the sake of keeping the refugees out of their country," Tarık Günersel says. "EU is important, but it has lost a lot of prestige, even among those who are pro-EU."
As an ominous sign, today's Cumhurriyet front page, which was printed before the arrests, read "Again, a coup against opposition".
To read our coverage of Turkey's coup attempt click here
To read our coverage of Turkey's 2015 election click here