Russian foreign ministry spokeswoman Maria Zakharova said the decisions of the ICC "have no meaning" for Russia.
"Russia is not a party to the Rome Statute of the International Criminal Court and bears no obligations under it," she said on Telegram.
"Russia does not cooperate with this body and possible 'recipes' for arrest coming from the international court will be legally void as far as we are concerned," Zakharova said, without referring to Putin by name.
Russia's former president Dmitry Medvedev also took to Twitter, likening the warrant to toilet paper.
The ICC announced earlier Friday it had issued an arrest warrant against Putin for the "unlawful deportation" of Ukrainian children.
The court had also issued a warrant against Maria Lvova-Belova, Russia's presidential commissioner for children's rights, on similar charges.
"There have been sanctions against me from all countries, even Japan, and now an arrest warrant...," Lvova-Belova was quoted as saying by state news agency RIA Novosti.
"But we will continue our work."
'Lock him up'
The head of the Investigative Committee, which probes major crimes, ordered a probe into the ICC warrants against "Russian citizens".
"Russia's Investigative Committee will identify specific individuals from among the ICC judges who made the obviously illegal decisions," investigators said in a statement.
Margarita Simonyan, head of the Russian state broadcaster RT, implied that Moscow could respond militarily to any attempts to arrest the Russian president.
"I would like to see the country that arrests Putin by the decision of the Hague. Some eight minutes after. Or however long the flight time will be to its capital," Simonyan said on social media.
Members of the Russian opposition praised the move.
"Congratulations to Vladimir Vladimirovich on his arrest in absentia! This is just the first step," Kremlin critic Mikhail Khodorkovsky, who spent a decade behind bars, said on social media.
"Lock him up!" tweeted activist Vladimir Milov, an ally of jailed opposition politician Alexei Navalny.