The suit seeks compensatory and punitive damages and injunctive relief for infringing Skechers' patents and design rights as well as for unfair competition, the company said in a statement.
Skechers also said it would take similar action against any retailer that sells Reebok's Walk Ahead RS shoes.
Reebok said on Thursday it does not comment on pending legal matters.
Skechers' Go Walk range starts at $40 for girls and around $60 for men and women, according to its website. Reebok's Walk Ahead RS women's shoes sell between $42.00 and $54.99 on Amazon.
Skechers filed the lawsuit in the U.S. District Court for the Central District of California.
Adidas has been losing market share to Nike. The market leader extended its lead to take 15 percent of the global sportswear market in 2013 compared with 10.8 percent for Adidas, according to data from Euromonitor, a market research firm.
Skechers' shares were down about 2 percent on Thursday on the New York Stock Exchange. (Click here to get the latest quotes.)