Personal-shopping service Stitch Fix has filed for an initial public offering, revealing that the six-year-old startup’s annual sales have zoomed to nearly $1 billion at a time when traditional clothing retailers are struggling.

The company, which selects and ships outfits to customers, said revenue surged to $977 million in the year ended July 29, from $73 million in 2014. Unlike most venture-backed startups, Stitch Fix has been profitable in recent years, though it swung to a $594,000 loss in the most recent year, the filing...