Smolyaninov said last October that he was no longer living in Russia.
His comments - made in an interview for Novaya Gazeta Europe, a newspaper now banned in Russia - drew condemnation from members of the Russian parliament, one of whom said the actor should be barred from all state-contracted films.
"For my part, I will appeal to the Investigative Committee with a request to initiate a criminal case against this traitor," lawmaker Biysultan Khamzaev told the RIA news agency.
The Investigative Committee said on Monday it had launched a criminal case against Smolyaninov after he took part in an interview with a "Western publication", but did not provide further details.
Since Russia invaded Ukraine in February 2022, dozens of actors and artists have fled abroad in fear of breaching the country's tough new laws on spreading "misinformation" about the war in Ukraine or discrediting the Russian army.
Moscow calls its actions in Ukraine a "special military operation" designed to demilitarise and "denazify" the country. Kyiv and its Western allies cast the invasion as an unprovoked act of aggression aimed at seizing territory.
