Opponents of the law say it is so vaguely worded that it could be used to target any of the social networking sites and blogs that make up Russia's most vibrant forum for opposition political debate.
"We are scared by the number of unarticulated points in the law and the lack of clear and transparent rules of the game," warned the general director of Russia's top social network VKontakte, Boris Dobrodeyev, quoted by the RIA Novosti news agency.
Under the new law, bloggers with more than 3,000 readers per day will be required to submit personal details to a special register.
The legislation bars blogs from "making calls to carry out terrorism or publicly justifying terrorism", carrying "other extremist materials" or promoting violence or pornography.
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One clause bans the distribution of information with the aim of "besmirching a citizen" based on their profession or political beliefs.
"That means you can't bad-mouth a political opponent or write something bad about the police," wrote blogger Andrei Malgin on the Echo of Moscow radio station's website.