The Food and Drug Administration isn’t just cracking down on e-cigarettes. Commissioner Scott Gottlieb also plans to pursue a ban on menthol cigarettes, according to senior agency officials.

It could take a year or more for a rule banning menthol to be finalized, and then another year for it to be enforceable in the marketplace. But a ban on menthols would be a big blow to British American Tobacco PLC, which sells the Newport brand of cigarettes in the U.S.

BAT’s...