Russia now requires Google, Facebook and other major internet companies based abroad to open offices in the country, after the president signed a law into effect on Thursday.
As of the turn of the year, all IT companies who reach more than 500,000 people on Russia and seek to reach an audience in the country must have a subsidiary there too.
The new law also applies to information and advertising in Russian.
The companies' subsidiaries are to be held accountable if the firm breaks Russian law, and are to cooperate with Russian authorities.
The text of the new law suggests it is likely to affect Twitter, YouTube and Instagram.
Companies found to be breaking the law would be penalized or could see their services blocked entirely in Russia.
The law drew criticism even as it was being planned. Stanislav Kozlovskiy, who heads Wikipedia in Russia, said he feared his company could theoretically be labelled a "foreign agent."
Media outlets and organizations in Russia are legally required to register as "foreign agents" if they are financed by money from abroad.
The Russian authorities have repeatedly fined Twitter in recent months, saying the platform has failed to delete calls to protests organized by the opposition.
Twitter's speed was also temporarily reduced as a further punitive measure.