Mr. Clendenin, 36, said he intends to "pursue other interests."
An Old Navy spokesman said a search was underway for his replacement.
Store sales dropping
The Gap Inc.'s discount division, like the rest of the chain, has been struggling.
Sales at Gap Inc. stores open for a year or longer have been dropping for the past 20 months.
Mr. Clendenin came to Old Navy from ESPN, where he was vice president of marketing.
Mr. Clendenin replaced the chain's founding marketing director, Richard Crisman, who had established the brand's offbeat advertising campaign with Magic the dog and a cast of celebrities including Old Navy's Old Lady, portrayed by the late fashion editor Carrie Donovan.