"People ram-raided my home before starting a fire to torch my house, where my wife and my two young children were sleeping," Mayor Vincent Jeanbrun said.
George Carneiro owns both properties that he is accused of having burnt down.
The visit, which was the largest since before the coronavirus pandemic, was held one year after Palestinians torched the shrine.
The emergencies ministry in Kurgan region near the border with Kazakhstan said 46 suspects had been identified and seven criminal cases had been initiated against alleged arsonists.
Independent news site SOTA blamed explosions and arson for some of the fires.
The fire came amid a spate of antisemitic incidents in Austin organized by the Goyim Defense League, a white supremacist group that holds antisemitic rallies.
The police received a call on Thursday night via the 100 emergency hotline about an attempt to set fire to the NII building in Kiryat Shmona.