Roskomnadzor in October threatened both Alphabet's Google and Meta's Facebook with fines based on a percentage of their annual turnover for a repeated failure to delete content that Moscow deems illegal.
Russian law allows for companies to be fined between 5% and 10% of annual turnover for repeated violations.
Moscow's Tagansky District Court said court dates for both companies - neither of which immediately responded to a request for comment - were set for Dec. 24.
Russia has increased pressure on foreign tech companies as it seeks to assert greater control over the Internet, slowing down Twitter since March and routinely fining others for content violations.
Google has paid more than 32 million roubles in fines this year. Google, Twitter and Meta have significantly reduced the number of posts prohibited by Moscow on their platforms.
Russia last month demanded that 13 foreign and mostly U.S. technology companies be officially represented on Russian soil by the end of 2021 or face possible restrictions or outright bans.
(Reporting by Alexander Marrow and Maria Kiselyova; Editing by Angus MacSwan)