Reebok, which is owned by German company Adidas AG, said 11 of Nike's styles for men and women infringed on the technology that allows shoes to collapse for travel or packaging purposes. Those shoes are marketed under the "Free," "Free Flex," "Free Zen & Now, "Free Trainer" and "Free Trail" product names.
The lawsuit, filed in U.S. District Court for the Eastern District of Texas, says Nike "willfully and intentionally" developed shoes using Reebok's technology.
A Nike spokesman said the company was evaluating the claims.
Adidas, the world's biggest maker of soccer shoes, acquired Reebok over a year ago to take on larger rival Nike on its home turf in the United States.
The company is also banking that Reebok's strength in sports lifestyle wear will complement Adidas' strength in classic sportswear.