The ice cream consists of vanilla ice cream, rum, fudge-covered rum balls and milk chocolate malt balls.
The company said the flavor is an homage to an old "Saturday Night Live" skit featuring Alec Baldwin as bakery owner Pete Schweddy. His unique holiday offerings included something called "Schweddy Balls."
Sean Greenwood, a spokesman for the Vermont ice cream maker, said Thursday that the company isn't worried about offending people with the name.
Schweddy Balls joins other oddly named flavors at Ben & Jerry's, including Karamel Sutra and Half Baked.
The Associated Press contributed to this report.
