Lawmakers in the State Duma, parliament's lower house, voted 320 to 15 to pass the proposed bill.
It is set to take effect on November 1 once it formally becomes law.
The proposed measures would create technology to monitor internet routing and steer Russian internet traffic away from foreign servers, ostensibly to prevent a foreign country from shutting it down.
Authors of the initiative say Russia must ensure the security of its networks after US President Donald Trump unveiled a new American cybersecurity strategy last year that said Russia had carried out cyber attacks with impunity.
The legislation has been dubbed a "sovereign internet" bill by Russian media. Critics say implementing the measures would be expensive and give vast censorship powers to the government's new traffic monitoring centre.
"It's a bill on digital slavery and the introduction of censorship for the web," said Sergei Ivanov, a member of the nationalist Liberal-Democratic Party.
The bill's authors insist however that the measures only outline a plan to make Russian internet "more secure and reliable".
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