The legislation was submitted to the State Duma Friday by Alexander Sidyakin, a member of the ruling United Russia party, RIA Novosti reported.
"If they want to turn their March of Millions into a riot, they should be ready to pay millions of rubles for this," Sidyakin said.
The State Duma will likely not discuss the legislation until 2013, said another member of United Russia.
"It is likely to be passed during Duma's spring session in 2013," Alexander Neverov, a United Russia's senior party official said.
The proposal came just a month after Sidyakin suggested increasing fines for protesters from $70 to $3,300 and making protesters participate in community service.
Russia has seen a wave of protests, some turning violent, since the country's December parliamentary elections and March 4 presidential election that saw a victory for Vladimir Putin.
A week ago, more than 400 protesters were arrested in a Moscow protest against Putin, during which protesters violently clashed with police.
Putin spokesman Dmitry Peskov hailed police actions, saying protesters "should have had their livers smeared on the sidewalk for injuring riot police."