Russia has repeatedly denied accusations that its forces have committed atrocities during its one-year-old invasion of its neighbor.
The ICC issued the warrant for Putin's arrest on suspicion of unlawful deportation of children and unlawful transfer of people from the territory of Ukraine to the Russian Federation.
The court also issued a warrant for Maria Lvova-Belova, Russia's Commissioner for Children's Rights, on the same charges.
In the first reaction to the news from Moscow, Russian foreign ministry spokeswoman Maria Zakharova said on her Telegram channel: "The decisions of the International Criminal Court have no meaning for our country, including from a legal point of view."
"Russia is not a party to the Rome Statute of the International Criminal Court and bears no obligations under it."
ICC prosecutor Karim Khan opened an investigation into possible war crimes, crimes against humanity and genocide in Ukraine a year ago. He highlighted during four trips to Ukraine that he was looking at alleged crimes against children and the targeting of civilian infrastructure.
The ICC move came a day after a U.N.-mandated investigative body accused Russia of committing wide-ranging war crimes in Ukraine, including wilful killings and torture, in some cases making children watch loved ones being raped and detaining others alongside dead bodies.
The news also came ahead of a planned state visit to Moscow next week by Chinese President Xi Jinping which is likely to cement much closer ties between Russia and China just as relations between Moscow and the West hit new lows.
Russia has been placed under unprecedented Western sanctions since he sent tens of thousands of troops into Ukraine on Feb. 24, 2022.