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”.
“The bill’s popular name — ‘The Chinese Firewall’ — has nothing to do with our initiative,” said Leonid Levin, a lawmaker from the ruling United Russia party which dominates Russian parliament.