The FSB claimed the group of six Russians was planning the "murder" of Russian TV and radio journalist Solovyov "on the instructions of the Security Service of Ukraine".
It added that the group "confessed to preparing the murder of Solovyov, after which they planned to flee abroad".
Solovyov has hosted prime-time political chat shows on Russian television since the late 1990s and has been decorated by the Russian government.
He has been sanctioned by the EU as a "propagandist" and has had villas seized by Italian financial police.
"What's surprising about this? I am on view to everyone," Solovyov said in comments on the alleged plot to the RIA Novosti news agency.
"I am a Jew and an anti-Fascist so it's obvious that I'm a target for (Ukrainian nationalist Stepan) Bandera-supporting, Nazi bastards," he added.
Speaking at a meeting of Russian prosecutors, President Vladimir Putin suggested Washington was involved in planning the "murder of a famous Russian TV journalist", without naming him.
"They have resorted to terror! To preparing the murders of our journalists. We know by name the curators of Western secret services, primarily, of course, from the CIA, who work with the security agencies of Ukraine," Putin said in televised remarks.
Molotov cocktails, Hitler portrait
"Apparently they give such advice (to kill journalists). So much for their attitude towards the rights of journalists... (and) human rights in general," Putin added.
A video recorded by the FSB aired on television showed security forces pushing half-naked young men onto the floor of flats and handcuffing them during searches.
According to the FSB, the officers found "fake" Ukrainian passports, pistols, drugs and Molotov cocktails, as well as a portrait of Hitler and a T-shirt with a swastika.
The footage also shows a handwritten note that suggests a Moscow TV studio complex was targeted.
A staunch supporter of Putin and Russia's military campaign in Ukraine, Solovyov has only questioned the navy's competence after the flagship cruiser Moskva sunk in the Black Sea off Odessa, leaving at least 28 dead or missing.
The video shows one of the men saying the group planned "murders of people who spout propaganda", naming a state television news anchor, Dmitry Kiselyov, and the editor-in-chief of Kremlin-funded broadcaster RT, Margarita Simonyan and her husband.