Is Amazon Europe’s next top model?

The online shop Zalando has trampled brick-and-mortar fashion retailers—and earned a market value topping $9 billion—by offering stylish wares from the likes of Tommy Hilfiger, Versace, and Adidas. Now, Zalando faces a rising internet threat of its own: Amazon.com. The online behemoth is picking up European market share as it signs up models and socialites and cozies up to such brands as Hugo Boss and Gucci. “We do more than people might appreciate,” says Susan Saideman, vice president for Amazon Fashion in Europe. Fashion “is very different from running a books business.”

Zalando is well-aware. Amazon now has 5.7 percent of the $42 billion online shoe and apparel market in Western Europe, according to researcher Euromonitor International—just behind Zalando’s 6.1 percent. Both have used high-fashion photo shoots, top models, and slick TV ads to pull almost even with leader Otto Group, a traditional mail-order catalog that has seen its share drop from 10 percent in 2011 to 6.2 percent this year.

Zalando is fighting back by beefing up distribution and sweetening its product mix. Early next year the company plans to open a warehouse near Paris that will shave a day or two off French deliveries. A few months later it will trim fulfillment costs by opening its first company-owned distribution center, a 1.4 million-square-foot facility in Poland, that will handle deliveries to cities across Europe. And Zalando says that over the past few months it’s increased the number of articles it sells by about a third, to 200,000.

For Christmas, the company has broadened its selection of such accessories as earrings, watches, and handbags and is making gift cards more widely available, says co-Chief Executive Officer Rubin Ritter. “In the past, we didn’t accentuate the Christmas business,” he says. This year he’s aiming to ensure there’s “a fresh assortment that’s always up to date.”

For now, Zalando has a fashion edge, according to a December analysis by Sanford C. Bernstein. While the sites have about the same number of brands in Germany, in the U.K., Zalando stocks nine of the top 20 womenswear brands, vs. Amazon’s four. And much of what Amazon carried in Europe was out of season or discounted, Bernstein found. Almost three-fifths of Amazon’s Levi’s products in Britain and Germany were discontinued merchandise, vs. just 14 percent at Zalando. Ritter says he’s working hard to strengthen relationships with major fashion brands—which typically prefer merchants that push current-season, full-price merchandise—as a way to keep interlopers at bay. “They know we are not out to commoditize or monopolize fashion,” he says. “We are focused on the more fashionable customer.”

A big challenge for Zalando will be spending enough to fend off Amazon while achieving its long-term goals of steadily increasing profit margins and sales growth that tops 20 percent annually—targets that have helped fuel a 64 percent share gain since its 2014 initial public offering. Zalando has promised a 4 percent to 5.5 percent operating margin this year, and analysts expect that to reach 6.5 percent in 2018. While Ritter says Zalando has been hitting its numbers even as competition picks up, UBS analyst Adam Cochrane says those forecasts look high in light of Amazon’s onslaught. UBS, which in November downgraded Zalando to “sell,” surveyed 1,000 German consumers last summer and found 78 percent said they’d shopped at Amazon for fashion in the past year, compared with 40 percent at Zalando. “The biggest investor fear for Zalando is Amazon improving its fashion offer and being a more credible threat,” Cochrane wrote in a November note.

Amazon’s Saideman recognizes she faces plenty of hurdles and says she’s working to improve access to the season’s hottest products. In November she visited new Hugo Boss CEO Mark Langer to see how Amazon could help as Boss pares its jumble of brands and reemphasizes office wear for men. And Amazon has launched a social marketing blitz. Hungarian model Barbara Palvin is doing photo shoots and promotions on YouTube. Italian fashion blogger Chiara Ferragni is promoting products including her own branded shoe line. And American socialite Olivia Palermo has recorded social media ads with Mr. Butler, her white Maltese dog.

That’s all part of Amazon’s effort to nurture a reputation as a place that’s trendy, not just cheap, says Saideman, who moved from Seattle to London in October. “Our mission is to be the place people go to discover fashion,” she says. “There’s not a strategy to be the discount house for online.”