The legislation allows the authorities to suspend and close down media outlets for libel and slander - punishment that is identical for news media found to be promoting alleged terrorism, extremism and racial hatred.
It also expands the definition for slander and libel to "dissemination of deliberately false information damaging individual honour and dignity".
The bill was submitted by Robert Schlegel, a former activist of Nashi, the Kremlin-backed youth movement that gained notoriety for street protests and political pranks against Putin critics.
Schlegel defended the measure, saying the law would create greater "justifications for allowing a media outlet to be shut down on a court's decision in cases of repeated dissemination of materials of a libellous nature".
Putin has presided over a steady rollback of post-Soviet media and political freedoms.
Major national television networks have come under the control of the Kremlin or its allies, and Russia's print media have also experienced growing official pressure.