Arrests were made in 12 cities across the country, with all suspects taken for questioning at the Security Directorate in capital Ankara, according to the Anadolu Agency in Turkey.
The arrests came after three men were apprehended in Spain suspected of being significant Anonymous players.
Anonymous has been active in taking on Governments it believes have infringed internet freedom.
Last Thursday, it claimed to have launched a successful Distributed Denial of Service (DDoS) attack on the Turkish Government, taking down a number of official websites.
Anonymous said it was concerned about internet censorship in the country, in particular plans “to implement a filter on internet browsing on 22 August under the pretense of protecting the youth from ‘harmful elements on the web.’”
“These acts of censorship are inexcusable. The internet is a platform for freedom, a place where anyone and everyone can come together, discuss topics, and share information, without the fear of government interference,” the group said in a release posted on the AnonOps blog.
“We, Anonymous, will not stand by and let this go unnoticed... Citizens of Turkey, Anonymous now fights with you."
Anonymous warned about a response to the arrests in Spain.
Over the weekend, the collective claimed to have launched a successful DDoS attack on the Spanish National Police website.
It claimed to have “paralysed the Official National Police website,” making it inaccessible for hours on Saturday.
“Arresting somebody for taking part in a DDoS attack is exactly like arresting somebody for attending a peaceful demonstration in their hometown. Anonymous believes this right to peacefully protest is one of the fundamental pillars of any democracy,” Anonymous said.
“You have not detained three participants of Anonymous. We have no members and we are not a group of any kind. You have, however, detained three civilians expressing themselves.”
In January, UK police arrested five males as part of an investigation into Anonymous' actions.