"The world received a signal that the Russian regime is criminal and its leadership and henchmen will be held accountable," Ukraine's Prosecutor General Andriy Kostin said on social media.
"This is a historic decision for Ukraine and the entire system of international law," Kostin added.
"World leaders will think three times before shaking his hand or sitting down at the negotiating table with him."
Ukraine's presidential chief of staff, Andriy Yermak, said the move was "just the beginning".
Ukrainian Foreign Minister Dmytro Kuleba also welcomed the news.
"(The) wheels of justice are turning. I applaud the ICC decision," Kuleba said.
"International criminals will be held accountable for stealing children and other international crimes."
Ukrainian presidential aide Mykhaylo Podolyak said the decision was "a clear signal to (Russian) elites of what will happen to them and why it won't be 'as before'."
EU foreign policy chief Josep Borrell on Friday hailed the International Criminal Court's arrest warrant for Russian President Vladimir Putin as an "important decision" for international justice and Ukraine's people.
"We have always made clear at the European Union, that those responsible for the illegal aggression against Ukraine must be brought to justice, and this International Criminal Court issue is just the start in the process of accountability," Borrell said.
The Hague-based ICC said it had also issued a warrant for Maria Lvova-Belova, Russia's presidential commissioner for children's rights.
Russia is not a member of the ICC. It was unclear how the ICC planned to enforce the warrant.
Former Russian President Dmitry Medvedev on Friday compared the International Criminal Court's arrest warrant for President Vladimir Putin to toilet paper.
"The International Criminal Court has issued an arrest warrant against Vladimir Putin. No need to explain WHERE this paper should be used," Medvedev said on Twitter, adding a toilet paper emoji.