The Reuters report says that Russian prosecutors asked a court to designate the US tech giant as an "extremist organisation," and the communications regulator said it would restrict access to Meta's Instagram starting 14 March.
The company said the decision would affect 80 million users in Russia.
"A criminal case has been initiated ... in connection with illegal calls for murder and violence against citizens of the Russian Federation by employees of the American company Meta, which owns the social networks Facebook and Instagram," Russia's Investigative Committee said.
The committee reports directly to President Vladimir Putin. It was not immediately clear what the consequences of the criminal case might be.
Reuters adds that Meta global affairs President Nick Clegg responded after the Russian government action with a tweeted statement saying that the company aimed to protect rights to speech as an expression of self-defence reacting to the invasion of Ukraine and that the policy only applied to Ukraine.
"If we applied our standard content policies without any adjustments we would now be removing content from ordinary Ukrainians expressing their resistance and fury at the invading military forces, which would rightly be viewed as unacceptable," Clegg wrote.
On 4 March Aljazeera reported that Russia had blocked access to Facebook. “The country’s communications regulator says it blocked Meta Platforms Inc’s Facebook in response to what it said were restrictions of access to Russian media on its platform, more than a week after Moscow invaded its neighbour Ukraine.
“The regulator, Roskomnadzor, said on Friday there had been 26 cases of discrimination against Russian media by Facebook since October 2020, with access restricted to state-backed channels like RT and the RIA news agency,” says the report by Aljazeera.