Social media reports that China is cracking down on travelers returning home with suitcases full of luxury goods have alarmed investors in companies ranging from Shiseido Co. to France's LVMH and Kering SA.

Shares of the fashion and cosmetics giants plunged as videos of border guards looking for imports over the duty-free allowance of 5,000 yuan ($727) spread on the web, adding to jitters stemming from a trade war with the U.S. Meanwhile, a traveler's customs receipt that's being shared widely on social media shows a customs levy of 60 percent on some cosmetics.

Chinese consumers make up the lion's share of growth for the luxury business and account for roughly a third of the industry's sales, according to consultancy Bain. Many do the bulk of their high-end shopping during visits to Tokyo, Seoul, Paris and other tourist destinations, where prices are lower than at home.