The suspects are members of the Socialist Platform of the Oppressed and the Marxist-Leninist Communist Party, Today's Zaman reported.
Eighteen were charged with damaging public property, and with membership in a terrorist organization, police said.
The seven other detainees were released, Today's Zaman said.
The suspects had participated in protests against Prime Minister Recep Tayyip Erdogan's plans to demolish the park and construct a mall.
The protests led to nationwide demonstrations that ended with Erdogan ordering riot police to clear the park.
Millions of Getty images now available for free via embed tool
Boston schools pull out free condoms over wrapping complaints