Reebok, based in Canton, Mass., has centered much of its business on toning shoes, which include its EasyTone walking shoes, RunTone running shoes and EasyTone flip flops.
The company claims the shoes, which have a rounded, slightly unstable sole, encourage strength by engaging more of a wearer's muscles.
Reebok made a number of claims in its advertising and marketing materials that the FTC said it could not support. That includes claims that its EasyTone footwear had been proven to lead to 28 percent more strength and tone in the buttock muscles and 11 percent more strength and tone in hamstring and calf muscles than regular walking shoes.
Under the settlement announced Wednesday, the athletic shoe and clothing maker is also barred from making any claims that the shoes add strength unless they are backed by scientific evidence.
A spokesman for Reebok, based in Canton, Mass., was not immediately available to comment. The company is owned by German shoe company Adidas.
Consumers seeking a refund will be paid either directly from the FTC or through a court-approved class-action lawsuit.
Online: To apply for a refund, go to http://1.usa.gov/pj2owK