The specific charges against Putin and the other official relate to the alleged abduction of Ukrainian children and teenagers during the conflict.
The warrants mark the first time that international charges have been issued for actions during the war between Russia and Ukraine.
The New York Times reports that the arrest warrants are unlikely to lead to the arrest of Putin or the other official, given the Russian government's resistance to the authority of the ICC.
However, the warrants send a strong signal that the international community will hold those responsible for war crimes accountable.
The move has been met with a range of responses from different parties.
Some see it as an opportunity to send a strong message to Russia and to elevate international law above political considerations.
Others argue that the ICC's jurisdiction is limited and the warrants are unlikely to have any practical impact.
Nonetheless, the warrants represent a significant development in the ongoing conflict between Russia and Ukraine, and may impact tensions between Russia and the West.