determined" that Russia had committed war crimes during the conflict in Ukraine, with Vice-President Kamala Harris saying in February that those involved would "be held to account".
The United Nations also released a report earlier this week that found Moscow's forced removal of Ukrainian children to areas under its control amounted to a war crime.
In a statement on Friday, the ICC said it had reasonable grounds to believe Mr Putin committed the criminal acts directly, as well as working with others. It also accused him of failing to use his presidential powers to stop children being deported.
Russia's commissioner for children's rights, Maria Lvova-Belova, is also wanted by the ICC for the same crimes.
ICC prosecutor Karim Khan has said the warrants were "based upon forensic evidence, scrutiny and what's been said by those two individuals".
The court had initially considered keeping the arrest warrants a secret, but decided to make them public to try and stop further crimes being committed.
"Children can't be treated as the spoils of war, they can't be deported," Mr Khan told the BBC.
"This type of crime doesn't need one to be a lawyer, one needs to be a human being to know how egregious it is."