This spring, the FDA took the first step toward implementing a rule that would ban menthol or other flavors from cigarette and e-cigarette products. It's unclear how long drafting and finalizing a menthol ban may take, but it's likely to take a year, if not longer. While the Tobacco Control Act says regulation shouldn't take effect for another year after it's finalized, a rule could go into effect earlier if it's deemed necessary to protect public health.

Analysts brushed aside concerns as mostly a headline risk since finalizing and implementing a rule could take years. However, they noted menthol cigarettes make up a sizable chunk of profits at British American Tobacco , Altria and Imperial Brands .

FDA Commissioner Dr. Scott Gottlieb plans to announce this week that the agency will move forward with a ban on menthol cigarettes in conjunction with a crackdown on e-cigarettes to curb "epidemic" levels of teen use, senior FDA officials told CNBC last week.

Tobacco stocks slid Monday as investors feared the consequences of a possible ban on menthol cigarettes, which the U.S. Food and Drug Administration is expected to propose this week.

British American Tobacco, which sells market leading menthol cigarette Newport, is seen as the most vulnerable company. Menthol cigarettes accounting for between 55 percent and 60 percent of its U.S. volumes, driving 25 percent to 27 percent of its global profit, according to estimates from Piper Jaffray analyst Michael Lavery. He estimates menthol cigarettes are about 18 percent to 20 percent of BAT's cigarette volumes and about 15 percent to 17 percent of profits.

BAT's operating profit is about 10 billion pounds (US$12.86 billion) on a run-rate basis, Lavery said. Last year, the company recorded an adjusted operating profit of 7.9 billion pounds (US$9 billion), he said, but that did not include a full year of the U.S. business, which BAT gained through its acquisition of Reynolds American.

Shares of BAT tumbled nearly 9 percent Monday. In an email to CNBC, a spokesman said the company was not aware of "anything that has changed to suggest the FDA would deviate from its existing multi-year comprehensive, rule-making process on flavors in tobacco products, which includes menthol."

"In any event, we look forward to continuing to participate in a thorough science-based review to address the use of flavors in tobacco products," he added.

Lavery estimates menthol accounts for 25 percent of Imperial Brands' volume, or 6 to 8 percent of its global profit. For fiscal year 2017, Imperial Brands reported about 3.8 billion pounds (US$4.89 billion) in operating profit, Lavery said.

Imperial Brands' stock fell about 2 percent Monday.

"Proposals to ban menthol cigarettes in the U.S. have been for the table for many years and we will continue to engage with the FDA on the topic," an Imperial Brands spokesman said in an email to CNBC. "We are aware of last week's renewed media reports regarding menthol tobacco products and will continue to monitor the situation, but until there's a formal update from the FDA, we'll decline to comment further."

Wells Fargo's Herzog estimates menthol represents about 21 percent of Altria's combustible cigarette volume, which totaled 116.61 billion sticks last year, according to a regulatory filing. Herzog also estimates menthol represents about 18 percent of Altria's total profit, which totaled $9.56 billion last year, according to the filing.

Shares of Altria fell 3.5 percent Monday. The company declined to comment, saying it was premature to comment without seeing the FDA's proposed actions.

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