Under the legislation that was passed in May, films containing "foul language" will be banned from wide release and books with swear words will have to be sold in sealed packages with obscenity warnings.
Theatres will not be allowed to stage productions containing obscenities according to the law, which imposes fines of up to 50,000 roubles ($US1500) for each infraction.
Russian media have reported that software known as the "swear-bot" will be used to police cursing on the Internet.
The law is meant to ensure "the protection and development of linguistic culture," according to a statement on the Kremlin's website. But critics say it is reminiscent of Soviet-era censorship and will suppress free expression.
Putin has struck a conservative tone in his latest presidential term, praising what he calls traditional values and holding up the Russian Orthodox Church as a moral authority.
Last month, newspaper Izvestiya said communications watchdog Roskomnadzor planned to use a search programme to root out rude words in online articles and comments attached to them.
The 25 million-rouble ($US729,500) system will search the 5000 mass media sites that are already monitored manually, the report said.
The "swear-bot" faces a huge task as Russian is known for the breadth and inventiveness of its obscene vocabulary.
A dictionary of Russian swear words lists over 1200 different phrases that use a single slang term for "penis".
Russian novelist Fyodr Dostoevsky wrote in the 19th century: "It's possible to express all thoughts, feelings and even deep analytical thoughts just by saying this one noun."
The swearing law follows stricter rules on bloggers and restrictions on non-state media that critics say were part of a campaign to bring independent media under Kremlin control, something the government denies.