Matilda, which is set to be released in October, has sparked harsh criticism from hard-line nationalists and some members of the Russian Orthodox Church.
They're offended by the film's depiction of the tsar, a man the Church deems a martyr.
Two cars were set on fire last week outside the office of the lawyer for the film's director and signs reading "burn for Matilda" were reportedly found near the scene.
Last month, assailants tried to set fire to the director's film studio.
Police spokeswoman Irina Volk said in a statement on Thursday that three of the detained have been charged with arson.
They include Alexander Kalinin, the leader of an obscure Christian Orthodox group who has publicly condoned the attacks.
Ministers have condemned some of the hostile reaction to the film about Tsar Nicholas.
