British American Tobacco (BAT) shares suffered the most, diving by almost 10 per cent in early trading, while Imperial Brands saw shares fall four per cent.
Analysts at Barclays estimate that U.S. sales of menthol cigarettes account for around 25% of BAT's annual underlying earnings and 11% for Imperial.
In a landmark move bound to further shake the tobacco industry, the Food and Drug Administration plans to propose a ban on menthol cigarettes next week as part of its aggressive campaign against flavored e-cigarettes and some tobacco products, agency officials said.
E-cigarettes and their liquid nicotine flavors would continue to be sold in dedicated vape stores, where the FDA believes age verification procedures are more reliable.
Given the FDA's position that it will follow a science-based approach, it is unlikely the regulatory body will outright ban menthol - although a proposal to restrict or lower the levels of menthol is reasonable, the analyst said.
Earlier this year, San Francisco passed a ban against the sales of menthol cigarettes and flavored e-cigarettes, as Fox Business also noted.
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Meanwhile, another report claims that the FDA also wants to ban flavored cartridges or pods used in e-cigarettes to crack down the increasing epidemic of vaping in teens.
"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.
The mooted ban, which could take up to two years to take effect, would be a massive blow for manufacturers of menthols such as British American Tobacco (BAT) and Imperial Brands.
Menthol cigarettes may soon become a thing of the past.
Imperial Brands Plc declined as much as 5 percent. The proportion is about 20 percent for Altria, according to the firm. Menthol cigarettes drive 25 percent to 27 percent of British American Tobacco's profit.
BAT shares have dropped 40% this year, the biggest drop in at least two decades.