Luxury brands are reeling from war-driven sales declines across the Persian Gulf region. LVMH reported demand for some brands fell as much as 70 percent in March as the conflict escalated. The world's largest luxury company is counting on wealthy Gulf elites to continue spending abroad while domestic tourism has slowed to a trickle.

Companies like Zegna and Hermès are moving inventory out of the region and into markets like London and Paris. Zegna executives hope expatriates who fled cities like Dubai and Manama will keep spending on luxury goods elsewhere. Meanwhile, Hermès has stopped or postponed deliveries to third-party stores in Qatar, Bahrain and Kuwait due to disrupted supply chains through Dubai's airport.

Before the war, annual sales in the Middle East were growing as much as 8 percent, according to Bernstein Research. Luxury executives still see the region as a long-term growth driver if tourist hubs can again attract travelers and expatriates return. But for now, brands are simply trying to mitigate the fallout while waiting for stability to return to this crucial multibillion-dollar market.