Members of the lower house, the Duma, passed the bill to prohibit the services from Russian territory if they were used to access blacklisted sites.
The bill instructs Russia’s telecommunications watchdog Roskomnadzor to compile a list of anonymiser services and prohibit any that fail to respect the bans issued in Russia on certain websites.
The proposed law still has to be approved by the upper chamber of parliament and then by President Vladimir Putin.
Several internet-based groups in Russia have condemned it as too vaguely formulated and too restrictive.
The Duma also approved moves Friday to oblige anyone using an online message service to identify themselves with a telephone number.
Russia’s opposition groups rely heavily on the internet to make up for their lack of access to the mainstream media.
But the Russian authorities have begun to tighten controls on online services, citing security concerns.
In June, Russian officials threatened to ban the Telegram messaging app after the FSB security service said those behind April’s deadly Saint Petersburg metro bombing had used it.
