Bruzzi is alleged to have grabbed and shaken the sculpture by artist Donia Maaoui because he felt its presence in the local church was offensive, Italian media reported.
Bruzzi was particularly upset because the work of art was placed under a crucifix. The sculpture was on display as part of the city's Marble Weeks festival.
Police called for calm after the city's mayor, Angelo Zubbani, waded in, saying the attack was "disgraceful".
"Nobody in our city, for whatever reason, should hide behind philosophical or ideological positions as a reason to damage work," he said.
Zubbani added that Carrara, in northern Italy, had a long history of welcoming artists to "sculpt and create beauty according to their tastes."