The law sets fines of up to 3,000 rubles ($94) for smoking in public places designated as no smoking areas. The steepest fines are reserved for offenders smoking in playgrounds.
Under the new rules, which are set to come into force on November 15, fines for vendors selling goods containing tobacco to minors have also been increased.
Public places affected by the change to the law include government buildings, healthcare and educational facilities, cultural sites and sports stadiums.
A total ban on smoking in restaurants, trains and hotels is set to come into effect next year.
The new law limits how stores can display products that contain tobacco. Sales from retail kiosks are to be banned from June 2014. Minimum prices will be set for cigarettes, some of which sell for as little as 40 rubles ($1.24) per pack.