The law called “sovereign internet” gives officials wide-ranging powers to restrict traffic on the Russian web.
The Kremlin has said the law will improve cyber security. A spokesman said users would not notice any change.
Russia is looking to route the country’s web traffic and data through state-controlled points, reducing reliance on foreign servers over which it has less control. Supporters say this is to protect the system from attacks from abroad.
To help with this project, the country is working on developing its own new address books so it can operate almost autonomously, although this work will not take effect until 2021.
Critics fear the Kremlin will try to create an internet firewall similar to that in China.
Cyber experts say it is unclear how the powers of the law might be used, or how effectively they can be implemented given the technology challenges and high costs.