Russia is not an ICC member country, meaning the court, located in The Hague, has no authority there.
However, it could affect Mr Putin in other ways, such as being unable to travel internationally. He could now be arrested if he sets foot in any of the court's 123 member states.
Mr Putin is only the third president to be issued with an ICC arrest warrant.
President Biden said that, while the court also held no sway in the US, the issuing of the warrant "makes a very strong point".
"He's clearly committed war crimes," he told reporters.