Seven people were arrested outside the Federation Council building in Moscow before council members unanimously approved the bill, RIA Novosti reported.
"We need to adopt this bill," Federation Council head Valentina Matvinenko said before the vote. "And believe me, no one has pressured me."
The bill will be sent on to Russian President Vladimir Putin, who has yet to say whether he will sign it, ITAR-Tass reported.
"In compliance with the law the president has two weeks to consider the document [after the Federation Council's approval]," presidential spokesman Dmitry Peskov said. "It depends on the Federation Council when the bill is submitted to the president for signature."
The proposed ban is in response to an act signed into U.S. law by President Barack Obama earlier this month, calling for sanctions against Russian officials suspected of human rights abuses, the Russian news agency RIA Novosti said.
The adoption ban bill is named after a two-year-old Russian boy, Dima Yakovlev, who died in 2008 after he was left in a hot car by his adoptive American father. The father was later acquitted of manslaughter.
Responding to the proposed bill, UNICEF executive director Anthony Lake urged the Russian government to be solely guided by the best interests of children in determining its policies, the U.N. News Service reported Wednesday.
"Let the best interests of children, and only their best interests, determine its actions," Lake said.