IPSWICH, England — The Ipswich Museum contains many alluring and potentially theft-worthy items, including a spectacular 2,000-year-old gold-leaf Egyptian death mask on loan from the British Museum and a rare Hawaiian cape featuring feathers from the extinct o’o bird. But when two thieves forced their way in after midnight on July 28, they were seeking something else entirely.

Never mind that their target, a large rhinoceros horn, was still attached to its owner, which had been standing blamelessly in the museum since 1907.

“They just snapped it off,” said Bryony Rudkin, the Ipswich Borough Council member in charge of culture. Grabbing a pair of additional horns (and the rhino skull they belonged to) from a shelf nearby, the thieves disappeared as quickly as they had come. “It was like ‘The Pink Panther,’ ” Ms. Rudkin said. “In and out.”

It might have seemed like a bizarre, anomalous incident, the act of someone with a perverse rhino fetish. But similar thefts, as many as 30 so far this year, have been reported in museums, galleries, antiques dealerships, auction houses and homes across Europe as criminals try to feed a growing demand in China and other Asian countries, where medicine made from ground rhino horns is believed to act as an aphrodisiac and to cure cancer and other diseases.