The Bill, which comes in the wake of legislation passed earlier this year that clamps down on beer commercials and advertising, was approved on Wednesday.
The measure now goes for a cursory third reading, before being submitted to the Upper House and President Vladimir Putin for his signature.
The law will ban drinking beer on streets, in stadiums, on public transportation, in parks or in other places where there are no cafés or restaurants.
Beer sales will be banned near schools and universities and to people under 18. Violators will be fined 100 rubles (about R20), or about four times the price of an average bottle of Russian beer.
It’s unclear when the Upper House will take up the measure.
Drinking vodka and hard alcohol in public is already illegal in Russia, and lawmakers have said the new legislation is appropriate given recent terrorist attacks and heightened security measures aimed at protecting the public.
Brewers say the law will be impossible to enforce, and have called the measure "a witch-hunt" pushed by the country’s powerful vodka industry.