Dubbed the "slapping law," it decriminalizes a first offense of domestic violence that does not seriously injure the person, making it a less serious administrative offense.
The punishment carries a fine of up to 30,000 rubles ($507), an arrest up to 15 days, or compulsory community service up to 120 hours.
In cases of repeated assaults, a defendant faces a fine of up to 40,000 rubles ($676), compulsory community service for up to six months, or being held under arrest for up to three months.
More than 85% of legislators in Russia's Duma approved the bill last month -- seen as part of Putin's drive to appease conservative pushing "traditional family values."
The bill's sponsors, including conservative senator Yelena Mizulina, believe the law would simply bring family law into line with reforms passed last summer that loosened punishment for other minor assaults.
Mizulina, a staunch proponent of traditional values, was also the author of Russia's controversial "gay propaganda law," which prohibits "propaganda of nontraditional sexual relationships."
The Russian Orthodox Church, with its emphasis on the traditional family, has also influenced the debate. As have the traditional rules of Russian family life, including the "domostroi," a centuries-old manual prescribing strict rules of behavior and requiring absolute submission to the head of the family.
'What we call home violence is not home violence'
A member of the Russian Duma Vitaly Milonov, who supported the law, told CNN: "I don't think that we should violate the rights of family and sometimes a man and a woman, wife and husband, have a conflict."
"Sometimes in this conflict they use, I don't know, a frying pan, uncooked spaghetti, and so on.
"Frankly speaking what we call home violence is not home violence -- it's sort of a new picture of family relations created by liberal media."
Human Rights Watch had urged parliament to reject the law, calling it "dangerous and incompatible with Russia's international human rights obligations."
"Universally gender based crimes are under-reported but in Russia they are hugely under reported," Yulia Gorbunova of Human Rights Watch told CNN on Tuesday.
"There is a stigma around talking about violence, physical violence at home and women do not feel that they can speak up.
"It is a very dangerous for the government to draw a line between 'just bruises' or serious physical violence because... the situation in Russia shows, that domestic violence very rarely ends with bruises. It usually almost always goes to the next step."
Official data on domestic violence in Russia is not centrally collected so it's difficult to verify. But state-run news agency RIA Novosti has reported that 40% of serious crimes in Russia are committed in the family, 36,000 women are beaten by their husbands daily, and 12,000 women die yearly as a result of domestic violence -- one woman every 44 minutes.