The bill bans people – even if they are single and heterosexual – in over a dozen countries from adopting Russian orphans.
The measure was unanimously passed in the Duma.
Fourteen countries, including Canada, Belgium, Spain, and Sweden, with France as the newest addition, have legalised same-sex marriage.
The bill, which comes amid a wider crackdown on foreign Russian adoptions, must still be passed in the upper chamber and signed by President Vladimir Putin, who has already backed the bill.
Last year, Russia banned adoptions for citizens of the United States, alleging neglect and mistreatment.
However, critics said it was in reprisal for a travel ban on Russian officials accused of rights violations.
With hundreds of adoptions each year between the two countries, the move sparked massive protests and petitions from thousands of people.
The newest additions to Russia’s family code prohibits adoptions from "persons in a marriage union between people of the same sex registered in a state where such a union is allowed, as well as citizens of such states that are not married".
This suggests that married heterosexual couples in countries with legalised same-sex marriage could still adopt from Russia.
A broader campaign defending “traditional values” is also sweeping the country. Last week, the Duma passed a bill that could imprison people seen as promoting homosexual “propaganda”.