The State Duma strongly backed a bill which also outlaws US-funded "non-profit organisations that engage in political activity", extending what critics say is a clampdown on Mr Putin's opponents since he returned to the presidency in May.
The new law is a response to US legislation known as the Magnitsky Act, passed by US Congress to impose visa bans and asset freezes on Russian officials accused of involvement in the death in custody of anti-corruption lawyer Sergei Magnitsky in 2009.
Mr Putin hinted at a news conference that he would sign the bill into law once the Senate votes on it next week, describing it as an emotional but appropriate response to an unfriendly move by the US.
"It is a myth that all children who land in American families are happy and surrounded by love," Olga Batalina, a deputy with Mr Putin's ruling United Russia party, said in defence of the new measures.
In a pointed echo of the Magnitsky Act, the Russian legislation has become known as the Dima Yakovlev law, after a Russian-born toddler who died after his American adoptive father left him locked in a sweltering car. It has outraged Russian liberals who say children are being made victims of politics. Some government officials, including Foreign Minister Sergei Lavrov, have expressed reservations about the legislation.
"Children should not be a bargaining chip in international affairs," said Mikhail Fedotov, the head of the Kremlin's human-rights council.
Last year, 962 Russian children from orphanages were adopted by Americans while more than 45,000 have found homes in the US since the 1991 Soviet collapse. Their parents are either dead or unable to care for them and some have complex medical needs.
The spat is overshadowing efforts to improve relations with US President Barack Obama's administration.
Signalling Moscow is worried about long-term damage to trade and diplomatic ties, Mr Lavrov has taken the rare step of appearing to stake out a view that differs from the Kremlin line. The Kremlin hopes Mr Obama will visit Russia for a summit in 2013.
In a debate reminiscent of the Cold War, deputies described foreign adoptions as an embarrassment, implying Russia could not care for its own.
The law was backed by 420 deputies and opposed by only seven in the 450-seat chamber. Its easy passage reflected a growing conservatism in society since Mr Putin's return to the presidency.
Critics say the new move will deprive children stuck in orphanages the chance of growing up in the care of families.
Some prominent non-governmental organisations will be threatened with closure as the law bans US-sponsored political NGOs from working in Russia. Russians who also hold US passports will be unable to lead such groups.
The US ambassador to Moscow, Michael McFaul, has responded to the new law, saying: "We are very concerned by measures... that would link the fate of orphaned children to unrelated political issues."
He said the bill, which still needs to be signed by Mr Putin before becoming law, would also "deprive Russian civil society activists engaged in 'political activities' of the ability to work with Americans of their choice".