“It’s Day 1 in the category,” Jeff Bezos, Amazon’s chief executive, said in a recent interview. Though characteristically tight-lipped on bottom-line details, Mr. Bezos said the company was making a “significant” investment in fashion to convince top brands that it wanted to work with them, not against them.

The traditional retail world — and many major brands that want no part of Amazon — are gearing up to fight for their lives.

“It has the latitude to set prices and charge whatever it wants,” Sucharita Mulpuru, an analyst for Forrester Research, said of Amazon. “That is a huge threat for brands.”

Amazon has sold clothing for years. But recently it has focused on signing on hundreds of contemporary and high-end brands, including Michael Kors, Vivienne Westwood, Catherine Malandrino, Jack Spade and Tracy Reese, and it continues to prowl for more. On Monday, some of Amazon’s muscle was on display as the company sponsored, and live-streamed, the Costume Institute Benefit at the Metropolitan Museum of Art and the accompanying exhibit. Mr. Bezos, the event’s honorary chairman, said that he was advised by Anna Wintour, Vogue’s editor, to wear a pocket square with his Tom Ford tuxedo (which is not available on Amazon). He did so.

Amazon’s decision to go after high fashion is about plain economics. Because Amazon’s costs are about the same whether it is shipping a $10 book or a $1,000 skirt, “gross profit dollars per unit will be much higher on a fashion item,” Mr. Bezos said, and it already makes money on fashion. While its MyHabit site, started last year, uses a flash-sale model to compete with Gilt Groupe, Mr. Bezos says the company’s new effort is not about selling clothes at deep discounts but at prices that ensure that “the designer brands are happy.”