The watchdog agency Roskomnadzor proposed the law, calling it a means of protecting children from offensive material.
Material carried ratings for age groups 16-and over, 18-and-over, and 21-and-over.
The media industry warned the law would face a number of challenges to interpretation and implementation, but the agency, Alexander Zharov, said this week he was not expecting many major problems.
"We are not going to be bullies showering everybody around with restrictions and warnings," Zharov said, adding, "I believe that every mass medium has an idea of how to use the law."
Roskomnadzor has suggested content creators, rather than broadcasters and publishers, make the call on the appropriate ratings, Russia's ITAR-Tass news agency said.