A group of thieves in Japan got a jump start on nabbing Apple Inc.’s iPhone 5 before anyone else in the world Friday morning.

At a time when thousands of eager Apple fans were already lined up outside outlets around the world, Osaka police said 191 of Apple’s latest must-have smartphone were stolen in the wee hours leading up to the official launch. As of Friday at noon, three stores were hit across Japan’s western metropolis in an unusual string of robberies targeting the hottest tech toy this fall.

Authorities...