British American Tobacco Plc, whose products include Newport, fell the most in more than four years in London, destroying 8.4 billion pounds ($10.8 billion) of market value.
Last year, BAT re-entered the USA market after a 12-year absence with the $47bn acquisition of Reynolds, owner of brands including Pall Mall, Newport and Camel, in a move that created the world's biggest tobacco company and was expected to speed up the development of e-cigarettes and vapes.
A senior U.S. Food and Drug Administration official said last week that the agency is looking at restricting menthol in traditional cigarettes.
E-cigarette products in mint, menthol and tobacco flavours will still be sold in retail outlets in the U.S. for now, because USA officials did not want to create a situation where cigarettes were more attractive to smokers who prefer a mint or menthol flavour.
BAT investors now fear for the future of the group's menthol United States brand, Newport, which it acquired when it bought RJ Reynolds previous year for $49bn (£38,1bn).
The potential menthol ban won't have a near-term effect on the markets, according to analysts.
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Earlier this year, San Francisco passed a ban against the sales of menthol cigarettes and flavored e-cigarettes, as Fox Business also noted.
The menthol proposal is just one of several initiatives the FDA plans to announce sometime next week, including a ban on sales of most flavored e-cigarettes at retail stores and gas stations across the country.
"It must be emphasised that at this stage these reports are still rumours and they make it clear that it would take some time to draw up the ban and then implement it", added Ian Forrest, investment research analyst at The Share Centre.
A study published last week in the academic journal Tobacco Control found that 6 percent of 15- to 17-year-olds used the popular e-cigarette brand JUUL within the last 30 days, and 11 percent had used an e-cigarette in general.
Menthol cigarettes may soon become a thing of the past. The proportion is about 20 percent for Altria, according to the firm.