Roskomnadzor, the regulator, said on Monday that the two social networks did not explain how and when they would comply with legislation requiring them to store Russian users' personal data on servers in Russia.
The news was first reported by Russia's Interfax news agency.
"The companies managing the social networks of Facebook and Twitter provided formal answers to our demands to confirm the localization of personal data of Russian users in Russia," Roskomnadzor told CNBC in an emailed comment Monday.
"They do not contain specifics about the actual implementation of the legislation at the current moment, nor about the timing of the implementation of these standards in the future."
The watchdog added: "In this regard, today Roskomnadzor begins administrative proceedings against both companies."
A Facebook spokesperson said the company is "in touch with relevant Russian governmental bodies regarding its activities in Russia." Twitter declined to comment.