Maker’s Mark Distillery Inc. claims the packaging for a bourbon-infused cigar misuses its red logo and dripping wax design.

Maker’s Mark asserts that the packaging for “The Bourbon Cigar” causes confusion. In a trademark infringement suit filed Jan. 8 in the U.S. District Court for the Western District of Kentucky, it seeks an injunction and damages from Spalding Group Inc., which does business as Ted’s Cigars.

Spalding had a license agreement with Maker’s Mark to manufacture cigars infused with its...