There was no immediate comment from Facebook.
A day earlier, a Russian court fined Alphabet Inc.'s Google 3 million roubles for violating personal data legislation and registered administrative proceedings against Facebook and Twitter for the same offence.
The cases are part of a wider spat between Russia and Big Tech, with Moscow routinely fining social media giants for failing to remove banned content and seeking to compel foreign tech firms to open offices in Russia.
WhatsApp could be fined between 1 million and 6 million roubles ($13,700 to $82,250), Interfax reported, citing court documents. A court date has not yet been set.
($1 = 72.9350 roubles)
(Reporting by Alexander Marrow; Editing by Alison Williams)