The title has been trademarked for alcoholic drinks in Russia before, but the RIA Novosti news agency said this is the first time someone had applied to use the name for actual firebombs.
Molotov cocktails were named after a Soviet foreign minister, Vyacheslav Molotov, in the run-up to World War II. The nickname applied to homemade bombs made of glass bottles filled with gasoline.
The Molotov cocktail has become a frequent part of ongoing anti-government demonstrations in Ukraine.
Citing a Moscow newspaper, RIA Novosti said the trademark would be registered in the petroleum products category if the request were granted, but chances are it will be denied because the term is widely used and therefore ineligible for trademark protection.