Shares in FTSE 100-listed BAT – valued at £76bn prior to Monday trading – fell by more than 9% on the report in the Wall Street Journal.
Rival Imperial Brands, which is worth £26bn and whose brands include Lambert & Butler and John Player Special, was down by more than 3%.
The Food and Drug Administration (FDA) was reported to be planning the ban on menthol cigarettes because they are harder to quit.
It has already announced plans to curb sales of flavoured e-cigarettes, seen as products that lure young people into smoking.
The menthol ban would impact BAT through its ownership of Newport cigarettes – one of the most popular menthol brands.
It acquired Newport as part of its $49bn purchase of RJ Reynolds last year.
Analysts at Barclays estimate that US sales of menthol cigarettes account for around 25% of BAT’s annual underlying earnings and 11% for Imperial.
But it is thought that a ban could take up to two years to come into force.
Nicholas Hyett, equity analyst at Hargreaves Lansdown, said: “Along with cigarette volumes shrinking, regulation is the other inevitable fact of the tobacco industry.
“The acquisition of Reynolds gave BAT a dominant position in US menthol.
“That’s a segment that’s been in regulators’ sights for some time – thanks to its perceived status as a gateway for new smokers.
“The FDA are now said to considering banning them altogether.
“While many menthol smokers would likely move over to non-menthol products, it would still be a major blow.”
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