Interfax reported the latest move in a growing crackdown on social networks who insist that publishing Russian propaganda is a bad thing are run by terrorists.
Russian authorities blocked access to Facebook last week under a new media law, but the "extremist" designation, if approved by a court, would effectively criminalise all of Meta's operations in Russia.
The company's Instagram app would also be blocked.
Earlier Friday, the speaker of the lower house of parliament, Vyacheslav Volodin, called on prosecutors to investigate Meta after Reuters reported that the company had temporarily eased internal restrictions on calling for violence against
Russian soldiers due to the invasion of Ukraine.
Russia has already banned certain social media companies like Facebook and Twitter, while tech companies have demonetised Russian state-sponsored media and blocked them in Europe.