Under the bill, the punishment for public dissemination of deliberately false information about issues that present a threat to public life and security as well as about measures taken to tackle this threat will vary depending on consequences of such a crime.
It may be punished by a fine from 300,000 ($3,825) to 700,000 ($8,925) rubles, up to 1 year of community service, or up to 3 years of imprisonment.
In addition, the upper house approved a bill on criminal liability of up to 7 years in prison for violating coronavirus quarantine rules.
The president is yet to sign the bills into law.
Russia registered 500 new cases in 24 hours, 387 of them in the capital, the national COVID-19 response centre said earlier in the day. The total number of cases has reached 2,337.