Vadym Novynskyi, whose wealth is estimated by Forbes at $1.4 billion, is one of the country's richest men, an ex-lawmaker and a sponsor of the Ukrainian Orthodox Church.
Footage shared by state media outlets showed a thin plume of dark smoke rising from the defense ministry's headquarters in Moscow.
The case of Moskalyov took a new twist when he vanished from his home during the night, hours before being sentenced to two years for discrediting the Russian armed forces.
"Everyone will have to do it in March."
The impact of the ICC's move to issue an arrest warrant on Putin - as well as Russia's children's rights commissioner - for the mass abduction of children from Ukraine remains unclear.
The Kremlin said Ukraine's treatment of the Orthodox Church, under the authority of the Moscow Patriarchate, is a reason for Russia's invasion.
Georgia's ruling party admitted the need to reduce "confrontation" in society as a reason for the bill's withdrawal.