The suspects, including the editor of the opposition Birgun newspaper Burak Ekici, were accused of "membership of an armed terrorist organization", Anadolu said. It said police were carrying out raids at the suspects' addresses.
The suspects were believed to be users of ByLock, an encrypted messaging app the government says was used by the network of US-based cleric Fethullah Gulen.
Gulen, whom Ankara blames for orchestrating the abortive coup, has denied involvement in the attempted military takeover.
Anadolu said the detention warrants were aimed at the media branch of Gulen's network. The identities of the other suspects were not immediately clear.
The ongoing crackdown, particularly against journalists, has alarmed rights groups and some of Turkey's Western allies, who fear the government is using the coup as a pretext to quash dissent.
Some 150,000 people have been sacked or suspended from jobs in the civil service and private sector and more than 50,000 have been detained for alleged links to the putsch.
Some 150 media outlets have also been shut down and around 160 journalists are in jail, according to the Turkish Journalists' Association.
The government, however, says the measures are necessary due to the gravity of the threats it faces.