The accused are suspected of causing damages to others and libelling them by sharing the rape allegations.
Three others wanted on the alleged offence are still at large. One of them is identified as Pramuk Anantasin, administrator of the FB page.
Earlier reports have identified Pramuk as living in the United States operating the page from there.
The 10 now in police custody have residence in Udon Thani, Bangkok, Nakhon Ratchasima, Pathum Thani, Nonthaburi, Pattalung and Chiang Mai.
The arrests followed the Court issuing an arrest warrant at the request of police.
Police have accused CSI LA90210, known among Thai netizens as CSI LA, of reporting false information concerning a rape claim by a 19-year-old Londoner, who alleged that she was drugged, robbed and raped during her vacation on Koh Tao island off Surat Thani province in June.
The alleged victim then filed a police complaint on nearby Koh Pangan island. It was still unclear why she did not file the complaint on Koh Tao.
She subsequently alleged that police there had refused to document the rape claim but accepted the robbery claim. Police deny that she had tried to file a rape complaint.
She then travelled back to London and informed her mother of the rape. The mother reportedly alerted UK police and handed over clothes that she claimed contained the DNA of the attackers.
When the complaint went public in UK media, Thai police set up an investigation team to probe the complaint and concluded the claimed rape had not occurred. However the FB page insisted otherwise.
Koh Tao had been infamous worldwide after two British backpackers were brutally killed in 2014.