Supporters of the art show have suggested the incident highlights the growing state influence of traditional, ultra-conservative elements of the Russian Orthodox Church, which has failed to condemn the attack.
In 2012 Russia introduced a law making it an offence to insult religious feelings, following the Pussy Riot "punk prayer protest".
According to the Times, the God's Will activists were questioned by police after the attack at the Manezhart gallery on August 14, but no charges were brought.
"Jesus Christ and the Virgin Mary are being mocked here," said the group's leader, Dmitry Enteo.
In a YouTube video Mr Enteo is shown vandalising a work by Megasoma Mars, The Beheading of St John the Baptist #2.
Russia's Human Rights Council has compared the actions to "barbarians from the Islamic State".
