If made law, the measure will put a 20% ceiling on any foreign stakes in Russian media, including those held indirectly through Russian partners.
Russia's main media outlets are state-owned or controlled by loyal oligarchs.
But top Putin ally Sergei Zheleznyak said Russia was facing "an information war unleashed against the country".
Russian TV news has accused the Ukrainian government of provoking clashes in eastern Ukraine through acts of aggression, including indiscriminate shelling of civilians.
The Kiev government blames pro-Russian separatists for the violence, and says Russia has fomented it by supplying soldiers and heavy weapons to the rebels.
The media bill is to go before Duma (lower house) deputies on 23 September, Itar-Tass news agency reports.
The restrictions would apply to magazines and internet publications as well as newspapers and broadcast media.
The bill is highly likely to become law as it was proposed by MPs who usually support the pro-Kremlin group United Russia.
BBC Monitoring reports that foreigners directly own stakes in some Russian mainstream media:

Bailey died after the incident at Cults Academy on 28 October.
The 16-year-old accused - who cannot be named for legal reasons - appeared in private at Aberdeen Sheriff Court.
The boy is also charged with having a blade or point on school premises. He made no plea, was fully committed and remanded in custody.
Special assemblies were held on Monday as pupils returned to classes for the first time since the incident.
Bailey's family issued a message of thanks for the support they have received.
A bill to restrict foreign ownership in Russia's media will soon go before the parliament, which is dominated by MPs loyal to President Vladimir Putin.
[NEXT_CONCEPT]
A teenage boy has appeared in court for a second time charged with murdering 16-year-old Bailey Gwynne, who was stabbed at his Aberdeen school.