BATS owns Newport, the largest menthol cigarette maker in North America, which contributes as much as 25% of the group’s annual profit.
Shares were down 9.3% to 3,008p, levels not seen in almost five years. The fall wiped the best part of £8bn from the company’s value.
A report in the Wall Street Journal on Friday night stated that US Food and Administration commissioner Scott Gottlieb wants to bring in tougher new rules over tobacco sales.
Much like e-cigarettes, menthol cigarettes are being targeted by officials because of their popularity among younger people.
A federal law banned flavoured cigarettes back in 2009, but the tobacco companies managed to win an exception for menthol, which was by far the most popular flavour.
Nicholas Hyett, equity analyst at Hargreaves Lansdown, said: "An ever more hostile regulatory environment might explain why BATS has decided to spend big on next generation products (NGPs) like e-vapour and heated tobacco. These products are believed to cause less harm to users, but even here the regulator is creating waves – potentially banning flavoured capsules popular with younger customers."
He added: "At 10.6 times expected earnings, the shares are trading well below their longer term average – although still some way above rival Imperial Brands In the past that’s been justified through BATS' presence in faster-growing emerging markets, as well as its strong position in NGPs. But with outsized exposure to a tough US tobacco market, emerging economies struggling, and with new vaping products also under scrutiny – BATS looks a higher-risk investment going forwards.”