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US President Barack Obama is expected to sign the Magnitsky Act into law, after the bill was approved by the US House of Representatives in November.
Named after Hermitage Capital lawyer Sergei Magnitsky, the legislation allows trade relations with Russia to continue even when Russians suspected of human rights abuses are denied access to the US.
Hermitage Capital chief Bill Browder called the vote "historic and definitive" and said it would "change the complexion of human rights in Russia for years to come".
Russian national Sergei Magnitsky, who was arrested in 2008 over fraud and tax evasion, died whilst in detention after having received a severe beating. The Magnitsky clause now allows any Russian connected to his arrest and death to be banned from travelling to the US and have their assets frozen.
A statement issued by the Russian Foreign Ministry following the vote said "there must be an answer from our side". Analysts expect the retaliatory bill could take the form of sanctions against US officials accused of violating the rights of Russian citizens.