HONG KONG — The group of 40 mainland Chinese tourists made all the requisite shopping purchases on a recent trip to Europe: silk scarves, Swiss watches, Louis Vuitton handbags.

And baby milk powder, of course. Loads of it.

Rushing shelves at a supermarket in Germany, Chinese shoppers stuffed a half-dozen large cans into bags, one of the tourists said. “One woman told me, ‘If it was easier to carry, we would buy more; it’s good and cheap here,’ ” recalled the tourist, Zhang Yuhua, 60, who bought two cans.

Chinese are buying up infant milk powder everywhere they can get it, outside of China. And that has led to shortages in at least a half-dozen countries, from the Netherlands to New Zealand. The lack of supply is a reminder of how the consumption patterns of Chinese — and their rising food and environmental safety concerns — can have far-reaching impacts on critical daily goods around the world.

Big retail chains like Boots and Sainsbury’s in Britain now limit individuals to two cans of infant formula per purchase, and customs officials in Hong Kong are enforcing a two-can, or four-pound, restriction on travelers taking it out of the territory — with violators facing fines of up to $6,500 and two years in prison.