The four unindentified suspects were charged with "abuse of power" while working for a mobile phone company for having passed on private information about subscribers and their call history, Azeri prosecutors said on August 19.
During a search of the home of one of the accused, investigators discovered "banned religious literature, disks, and brochures containing speeches by Fethullah Gulen," they said.
A close ally of Ankara, Baku earlier this week opened a criminal investigation into supporters of Gulen, who Turkish President Recep Tayyip Erdogan believes tried to remove him from power on July 15.
The cleric, living in self-imposed exile in the United States, vehemently denies it.
Azerbaijan last month shut down a private television channel over plans to broadcast an interview with Gulen to avoid provoking Turkey.
Gulen's Hizmet movement has started schools around the world, including in ex-Soviet Kazakhstan, funded by the cleric's followers.
Separately, Bloomberg reported that the U.S. Justice Department has sent representatives to Turkey to investigate claims made in connection with Turkey's request to extradite Gulen.
Comment: See also: Turkish coup attempt, what was behind it?