Roskomnadzor chief Alexander Zharod told reporters on Tuesday that foreign Internet companies would be forced to comply with the data storage requirement, Bloomberg reported.
Else, they would be asked to pack their bags, he added.
A law was signed by President Vladimir Putin three years ago requiring foreign technology companies to retain data of Russians on servers located within the country.
Last November, Roskomnadzor ordered Russian service providers to block access to LinkedIn because the company had not complied with this law.
In the United States, technology companies have been trying to fight orders to turn over data stored abroad.
Microsoft won a case over emails stored in Ireland but is now facing a challenge in Supreme Court.